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Cross-validation (statistics)
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Diagram of k-fold cross-validation with k=4.
Cross-validation, sometimes called rotation estimation,[1][2][3] or out-of-sample testing is any of various similar model validation techniques for assessing how the results of a statistical analysis will generalize to an independent data set. It is mainly used in settings where the goal is prediction, and one wants to estimate how accurately a predictive model will perform in practice. In a prediction problem, a model is usually given a dataset of known data on which training is run (training dataset), and a dataset of unknown data (or first seen data) against which the model is tested (called the validation dataset or testing set).[4],[5] The goal of cross-validation is to test the model’s ability to predict new data that was not used in estimating it, in order to flag problems like overfitting or selection bias[6] and to give an insight on how the model will generalize to an independent dataset (i.e., an unknown dataset, for instance from a real problem).
One round of cross-validation involves partitioning a sample of data into complementary subsets, performing the analysis on one subset (called the training set), and validating the analysis on the other subset (called the validation set or testing set). To reduce variability, in most methods multiple rounds of cross-validation are performed using different partitions, and the validation results are combined (e.g. averaged) over the rounds to give an estimate of the model’s predictive performance.
In summary, cross-validation combines (averages) measures of fitness in prediction to derive a more accurate estimate of model prediction performance.[7]
Contents
1 Purpose of cross-validation
2 Common types of cross-validation
2.1 Exhaustive cross-validation
2.1.1 Leave-p-out cross-validation
2.1.2 Leave-one-out cross-validation
2.2 Non-exhaustive cross-validation
2.2.1 k-fold cross-validation
2.2.2 Holdout method
2.2.3 Repeated random sub-sampling validation
3 Measures of fit
4 Statistical properties
5 Computational issues
6 Limitations and misuse
7 Cross validation for time-series models
8 Applications
9 See also
10 Notes and references
Purpose of cross-validation[edit]
Suppose we have a model with one or more unknown parameters, and a data set to which the model can be fit (the training data set). The fitting process optimizes the model parameters to make the model fit the training data as well as possible. If we then take an independent sample of validation data from the same population as the training data, it will generally turn out that the model does not fit the validation data as well as it fits the training data. The size of this difference is likely to be large especially when the size of the training data set is small, or when the number of parameters in the model is large. Cross-validation is a way to estimate the size of this effect.
In linear regression we have real response values y1, ..., yn, and n p-dimensional vector covariates x1, ..., xn. The components of the vectors xi are denoted xi1, ..., xip. If we use least squares to fit a function in the form of a hyperplane y = a + βTx to the data (xi, yi) 1 ≤ i ≤ n, we could then assess the fit using the mean squared error (MSE). The MSE for given estimated parameter values a and β on the training set (xi, yi) 1 ≤ i ≤ n is
1 n ∑ i = 1 n ( y i − a − β T x i ) 2 = 1 n ∑ i = 1 n ( y i − a − β 1 x i 1 − ⋯ − β p x i p ) 2 {\displaystyle {\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-a-{\boldsymbol {\beta }}^{T}\mathbf {x} _{i})^{2}={\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-a-\beta _{1}x_{i1}-\dots -\beta _{p}x_{ip})^{2}}
If the model is correctly specified, it can be shown under mild assumptions that the expected value of the MSE for the training set is (n − p − 1)/(n + p + 1) < 1 times the expected value of the MSE for the validation set[8] (the expected value is taken over the distribution of training sets). Thus if we fit the model and compute the MSE on the training set, we will get an optimistically biased assessment of how well the model will fit an independent data set. This biased estimate is called the in-sample estimate of the fit, whereas the cross-validation estimate is an out-of-sample estimate.
Since in linear regression it is possible to directly compute the factor (n − p − 1)/(n + p + 1) by which the training MSE underestimates the validation MSE under the assumption that the model specification is valid, cross-validation can be used for checking whether the model has been overfitted, in which case the MSE in the validation set will substantially exceed its anticipated value. (Cross-validation in the context of linear regression is also useful in that it can be used to select an optimally regularized cost function). In most other regression procedures (e.g. logistic regression), there is no simple formula to compute the expected out-of-sample fit. Cross-validation is, thus, a generally applicable way to predict the performance of a model on unavailable data using numerical computation in place of theoretical analysis.
Common types of cross-validation[edit]
Two types of cross-validation can be distinguished, exhaustive and non-exhaustive cross-validation.
Exhaustive cross-validation[edit]
Exhaustive cross-validation methods are cross-validation methods which learn and test on all possible ways to divide the original sample into a training and a validation set.
Leave-p-out cross-validation[edit]
Leave-p-out cross-validation (LpO CV) involves using p observations as the validation set and the remaining observations as the training set. This is repeated on all ways to cut the original sample on a validation set of p observations and a training set.
LpO cross-validation requires training and validating the model C p n {\displaystyle C_{p}^{n}} times, where n is the number of observations in the original sample, and where C p n {\displaystyle C_{p}^{n}} is the binomial coefficient. For p > 1 and for even moderately large n, LpO CV can become computationally infeasible. For example, with n = 100 and p = 30 = 30 percent of 100 (as suggested above), C 30 100 ≈ 3 × 10 25 . {\displaystyle C_{30}^{100}\approx 3\times 10^{25}.}
Leave-one-out cross-validation[edit]
Leave-one-out cross-validation (LOOCV) is a particular case of leave-p-out cross-validation with p = 1.
The process looks similar to jackknife; however, with cross-validation one computes a statistic on the left-out sample(s), while with jackknifing one computes a statistic from the kept samples only.
LOO cross-validation requires less computation time than LpO cross-validation because there are only C 1 n = n {\displaystyle C_{1}^{n}=n} passes rather than C k n {\displaystyle C_{k}^{n}} . However, n {\displaystyle n} passes may still require quite a large computation time, in which case other approaches such as k-fold cross validation may be more appropriate.
Pseudo-Code-Algorithm:
Input:
x, {vector of length N with x-values of data points}
y, {vector of length N with y-values of data points}
Output:
err, {estimate for the prediction error}
Steps:
err ← 0
for i ← 1, . . . , N do
// define the cross-validation subsets
x_in ← (x[1], . . . , x[i − 1], x[i + 1], . . . , x[N])
y_in ← (y[1], . . . , y[i − 1], y[i + 1], . . . , y[N]
x_out ← x[i]
interpolate(x_in, y_in, x_out, y_out)
err ← err + (y[i] − y_out)^2
end for
err ← err/N
Non-exhaustive cross-validation[edit]
Non-exhaustive cross validation methods do not compute all ways of splitting the original sample. Those methods are approximations of leave-p-out cross-validation.
k-fold cross-validation[edit]
In k-fold cross-validation, the original sample is randomly partitioned into k equal sized subsamples. Of the k subsamples, a single subsample is retained as the validation data for testing the model, and the remaining k − 1 subsamples are used as training data. The cross-validation process is then repeated k times, with each of the k subsamples used exactly once as the validation data. The k results can then be averaged to produce a single estimation. The advantage of this method over repeated random sub-sampling (see below) is that all observations are used for both training and validation, and each observation is used for validation exactly once. 10-fold cross-validation is commonly used,[9] but in general k remains an unfixed parameter.
For example, setting k = 2 results in 2-fold cross-validation. In 2-fold cross-validation, we randomly shuffle the dataset into two sets d0 and d1, so that both sets are equal size (this is usually implemented by shuffling the data array and then splitting it in two). We then train on d0 and validate on d1, followed by training on d1 and validating on d0.
When k = n (the number of observations), the k-fold cross-validation is exactly the leave-one-out cross-validation.
In stratified k-fold cross-validation, the folds are selected so that the mean response value is approximately equal in all the folds. In the case of binary classification, this means that each fold contains roughly the same proportions of the two types of class labels.
Holdout method[edit]
In the holdout method, we randomly assign data points to two sets d0 and d1, usually called the training set and the test set, respectively. The size of each of the sets is arbitrary although typically the test set is smaller than the training set. We then train (build a model) on d0 and test (evaluate its performance) on d1.
In typical cross-validation, results of multiple runs of model-testing are averaged together; in contrast, the holdout method, in isolation, involves a single run. It should be used with caution because without such averaging of multiple runs, one may achieve highly misleading results. One's indicator of predictive accuracy (F*), as noted below, will tend to be unstable since it will not be smoothed out by multiple iterations. Similarly, indicators of the specific role played by various predictor variables (e.g., values of regression coefficients) will tend to be unstable.
While the holdout method can be framed as "the simplest kind of cross-validation",[10] many sources instead classify holdout as a type of simple validation, rather than a simple or degenerate form of cross-validation.[2][11]
Repeated random sub-sampling validation[edit]
This method, also known as Monte Carlo cross-validation,[12] randomly splits the dataset into training and validation data. For each such split, the model is fit to the training data, and predictive accuracy is assessed using the validation data. The results are then averaged over the splits. The advantage of this method (over k-fold cross validation) is that the proportion of the training/validation split is not dependent on the number of iterations (folds). The disadvantage of this method is that some observations may never be selected in the validation subsample, whereas others may be selected more than once. In other words, validation subsets may overlap. This method also exhibits Monte Carlo variation, meaning that the results will vary if the analysis is repeated with different random splits.
As the number of random splits approaches infinity, the result of repeated random sub-sampling validation tends towards that of leave-p-out cross-validation.
In a stratified variant of this approach, the random samples are generated in such a way that the mean response value (i.e. the dependent variable in the regression) is equal in the training and testing sets. This is particularly useful if the responses are dichotomous with an unbalanced representation of the two response values in the data.
Measures of fit[edit]
The goal of cross-validation is to estimate the expected level of fit of a model to a data set that is independent of the data that were used to train the model. It can be used to estimate any quantitative measure of fit that is appropriate for the data and model. For example, for binary classification problems, each case in the validation set is either predicted correctly or incorrectly. In this situation the misclassification error rate can be used to summarize the fit, although other measures like positive predictive value could also be used. When the value being predicted is continuously distributed, the mean squared error, root mean squared error or median absolute deviation could be used to summarize the errors.
Statistical properties[edit]
Suppose we choose a measure of fit F, and use cross-validation to produce an estimate F* of the expected fit EF of a model to an independent data set drawn from the same population as the training data. If we imagine sampling multiple independent training sets following the same distribution, the resulting values for F* will vary. The statistical properties of F* result from this variation.
The cross-validation estimator F* is very nearly unbiased for EF [13][citation needed]. The reason that it is slightly biased is that the training set in cross-validation is slightly smaller than the actual data set (e.g. for LOOCV the training set size is n − 1 when there are n observed cases). In nearly all situations, the effect of this bias will be conservative in that the estimated fit will be slightly biased in the direction suggesting a poorer fit. In practice, this bias is rarely a concern.
The variance of F* can be large.[14][15] For this reason, if two statistical procedures are compared based on the results of cross-validation, it is important to note that the procedure with the better estimated performance may not actually be the better of the two procedures (i.e. it may not have the better value of EF). Some progress has been made on constructing confidence intervals around cross-validation estimates,[14] but this is considered a difficult problem.
Computational issues[edit]
Most forms of cross-validation are straightforward to implement as long as an implementation of the prediction method being studied is available. In particular, the prediction method can be a "black box" – there is no need to have access to the internals of its implementation. If the prediction method is expensive to train, cross-validation can be very slow since the training must be carried out repeatedly. In some cases such as least squares and kernel regression, cross-validation can be sped up significantly by pre-computing certain values that are needed repeatedly in the training, or by using fast "updating rules" such as the Sherman–Morrison formula. However one must be careful to preserve the "total blinding" of the validation set from the training procedure, otherwise bias may result. An extreme example of accelerating cross-validation occurs in linear regression, where the results of cross-validation have a closed-form expression known as the prediction residual error sum of squares (PRESS).
Limitations and misuse[edit]
Cross-validation only yields meaningful results if the validation set and training set are drawn from the same population and only if human biases are controlled.
In many applications of predictive modeling, the structure of the system being studied evolves over time (i.e. it is "non-stationary"). Both of these can introduce systematic differences between the training and validation sets. For example, if a model for predicting stock values is trained on data for a certain five-year period, it is unrealistic to treat the subsequent five-year period as a draw from the same population. As another example, suppose a model is developed to predict an individual's risk for being diagnosed with a particular disease within the next year. If the model is trained using data from a study involving only a specific population group (e.g. young people or males), but is then applied to the general population, the cross-validation results from the training set could differ greatly from the actual predictive performance.
In many applications, models also may be incorrectly specified and vary as a function of modeler biases and/or arbitrary choices. When this occurs, there may be an illusion that the system changes in external samples, whereas the reason is that the model has missed a critical predictor and/or included a confounded predictor. New evidence is that cross-validation by itself is not very predictive of external validity, whereas a form of experimental validation known as swap sampling that does control for human bias can be much more predictive of external validity.[16] As defined by this large MAQC-II study across 30,000 models, swap sampling incorporates cross-validation in the sense that predictions are tested across independent training and validation samples. Yet, models are also developed across these independent samples and by modelers who are blinded to one another. When there is a mismatch in these models developed across these swapped training and validation samples as happens quite frequently, MAQC-II shows that this will be much more predictive of poor external predictive validity than traditional cross-validation.
The reason for the success of the swapped sampling is a built-in control for human biases in model building. In addition to placing too much faith in predictions that may vary across modelers and lead to poor external validity due to these confounding modeler effects, these are some other ways that cross-validation can be misused:
By performing an initial analysis to identify the most informative features using the entire data set – if feature selection or model tuning is required by the modeling procedure, this must be repeated on every training set. Otherwise, predictions will certainly be upwardly biased.[17] If cross-validation is used to decide which features to use, an inner cross-validation to carry out the feature selection on every training set must be performed.[18]
By allowing some of the training data to also be included in the test set – this can happen due to "twinning" in the data set, whereby some exactly identical or nearly identical samples are present in the data set. Note that to some extent twinning always takes place even in perfectly independent training and validation samples. This is because some of the training sample observations will have nearly identical values of predictors as validation sample observations. And some of these will correlate with a target at better than chance levels in the same direction in both training and validation when they are actually driven by confounded predictors with poor external validity. If such a cross-validated model is selected from a k-fold set, human confirmation bias will be at work and determine that such a model has been validated. This is why traditional cross-validation needs to be supplemented with controls for human bias and confounded model specification like swap sampling and prospective studies.
Cross validation for time-series models[edit]
Since the order of the data is important, cross-validation might be problematic for time-series models. A more appropriate approach might be to use forward chaining.
Applications[edit]
Cross-validation can be used to compare the performances of different predictive modeling procedures. For example, suppose we are interested in optical character recognition, and we are considering using either support vector machines (SVM) or k nearest neighbors (KNN) to predict the true character from an image of a handwritten character. Using cross-validation, we could objectively compare these two methods in terms of their respective fractions of misclassified characters. If we simply compared the methods based on their in-sample error rates, the KNN method would likely appear to perform better, since it is more flexible and hence more prone to overfitting[citation needed] compared to the SVM method.
Cross-validation can also be used in variable selection.[19] Suppose we are using the expression levels of 20 proteins to predict whether a cancer patient will respond to a drug. A practical goal would be to determine which subset of the 20 features should be used to produce the best predictive model. For most modeling procedures, if we compare feature subsets using the in-sample error rates, the best performance will occur when all 20 features are used. However under cross-validation, the model with the best fit will generally include only a subset of the features that are deemed truly informative.
A recent development in medical statistics is its use in meta-analysis. It forms the basis of the validation statistic, Vn which is used to test the statistical validity of meta-analysis summary estimates.[20] It has also been used in a more conventional sense in meta-analysis to estimate the likely prediction error of meta-analysis results.[21]
See also[edit]
Wikimedia Commons has media related to Cross-validation (statistics).
Boosting (machine learning)
Bootstrap aggregating (bagging)
Bootstrapping (statistics)
Model selection
Resampling (statistics)
Stability (learning theory)
Validity (statistics)
Notes and references[edit]
Jump up ^ Geisser, Seymour (1993). Predictive Inference. New York, NY: Chapman and Hall. ISBN 0-412-03471-9.
^ Jump up to: a b Kohavi, Ron (1995). "A study of cross-validation and bootstrap for accuracy estimation and model selection". Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence. San Mateo, CA: Morgan Kaufmann. 2 (12): 1137–1143. CiteSeerX 10.1.1.48.529.
Jump up ^ Devijver, Pierre A.; Kittler, Josef (1982). Pattern Recognition: A Statistical Approach. London, GB: Prentice-Hall.
Jump up ^ "What is the difference between test set and validation set?". Retrieved 10 October 2018.
Jump up ^ "Newbie question: Confused about train, validation and test data!". Archived from the original on 2015-03-14. Retrieved 2013-11-14. CS1 maint: BOT: original-url status unknown (link)
Jump up ^ Cawley, Gavin C.; Talbot, Nicola L. C. (2010). "On Over-fitting in Model Selection and Subsequent Selection Bias in Performance Evaluation" (PDF). 11. Journal of Machine Learning Research: 2079–2107.
Jump up ^ Grossman,, Robert; Seni, Giovanni; Elder, John; Agarwal, Nitin; Liu, Huan (2010). Ensemble Methods in Data Mining: Improving Accuracy Through Combining Predictions. Morgan & Claypool. doi:10.2200/S00240ED1V01Y200912DMK002.
Jump up ^ Trippa, Lorenzo; Waldron, Levi; Huttenhower, Curtis; Parmigiani, Giovanni (March 2015). "Bayesian nonparametric cross-study validation of prediction methods". The Annals of Applied Statistics. 9 (1): 402–428. arXiv:1506.00474. doi:10.1214/14-AOAS798. ISSN 1932-6157.
Jump up ^ McLachlan, Geoffrey J.; Do, Kim-Anh; Ambroise, Christophe (2004). Analyzing microarray gene expression data. Wiley.
Jump up ^ "Cross Validation". Retrieved 11 November 2012.
Jump up ^ Arlot, Sylvain; Celisse, Alain (2010). "A survey of cross-validation procedures for model selection". Statistics Surveys. 4: 40–79. In brief, CV consists in averaging several hold-out estimators of the risk corresponding to different data splits.
Jump up ^ Dubitzky,, Werner; Granzow, Martin; Berrar, Daniel (2007). Fundamentals of data mining in genomics and proteomics. Springer Science & Business Media. p. 178.
Jump up ^ "Thoughts on prediction and cross-validation." Ronald Christensen, Department of Mathematics and Statistics University of New Mexico, May 21, 2015. Retrieved from http://www.math.unm.edu/~fletcher/Prediction.pdf on May 31, 2017.
^ Jump up to: a b Efron, Bradley; Tibshirani, Robert (1997). "Improvements on cross-validation: The .632 + Bootstrap Method". Journal of the American Statistical Association. 92 (438): 548–560. doi:10.2307/2965703. JSTOR 2965703. MR 1467848.
Jump up ^ Stone, Mervyn (1977). "Asymptotics for and against cross-validation". Biometrika. 64 (1): 29–35. doi:10.1093/biomet/64.1.29. JSTOR 2335766. MR 0474601.
Jump up ^ Consortium, MAQC (2010). "The Microarray Quality Control (MAQC)-II study of common practices for the development and validation of microarray-based predictive models". Nature Biotechnology. London: Nature Publishing Group. 28: 827–838. doi:10.1038/nbt.1665. PMC 3315840. PMID 20676074.
Jump up ^ Bermingham, Mairead L.; Pong-Wong, Ricardo; Spiliopoulou, Athina; Hayward, Caroline; Rudan, Igor; Campbell, Harry; Wright, Alan F.; Wilson, James F.; Agakov, Felix; Navarro, Pau; Haley, Chris S. (2015). "Application of high-dimensional feature selection: evaluation for genomic prediction in man". Sci. Rep. 5: 10312. Bibcode:2015NatSR...510312B. doi:10.1038/srep10312.
Jump up ^ Varma, Sudhir; Simon, Richard (2006). "Bias in error estimation when using cross-validation for model selection". BMC Bioinformatics. 7: 91. doi:10.1186/1471-2105-7-91. PMC 1397873. PMID 16504092.
Jump up ^ Picard, Richard; Cook, Dennis (1984). "Cross-Validation of Regression Models". Journal of the American Statistical Association. 79 (387): 575–583. doi:10.2307/2288403. JSTOR 2288403.
Jump up ^ Willis BH, Riley RD (2017). "Measuring the statistical validity of summary meta-analysis and meta-regression results for use in clinical practice" (PDF). Statistics in Medicine. 36 (21): 3283–3301. doi:10.1002/sim.7372. PMC 5575530. PMID 28620945.
Jump up ^ Riley RD, Ahmed I, Debray TP, Willis BH, Noordzij P, Higgins JP, Deeks JJ (2015). "Summarising and validating test accuracy results across multiple studies for use in clinical practice" (PDF). Statistics in Medicine. 34 (13): 2081–2103. doi:10.1002/sim.6471. PMC 4973708. PMID 25800943. CS1 maint: Multiple names: authors list (link)
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Telecommunications in South Africa
From Wikipedia, the free encyclopedia
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This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (January 2012) (Learn how and when to remove this template message)
Suburban communication towers in Pretoria
Telecommunications infrastructure in South Africa provides modern and efficient service to urban areas, including cellular and internet services. In 1997, Telkom, the South African telecommunications parastatal, was partly privatised and entered into a strategic equity partnership with a consortium of two companies, including SBC, a U.S. telecommunications company. In exchange for exclusivity (a monopoly) to provide certain services for 5 years, Telkom assumed an obligation to facilitate network modernisation and expansion into the unserved areas[citation needed].
A Second Network Operator was to be licensed to compete with Telkom across its spectrum of services in 2002, although this license was only officially handed over in late 2005 and has recently begun operating under the name, Neotel[citation needed]. Four cellular companies provide service to over 30 million subscribers, with South Africa considered to have the 4th most advanced mobile telecommunications network worldwide[citation needed]. The five cellular providers are Vodacom, MTN, Cell C, Telkom (Mobile), which is run by Telkom[1][2], and from early 2018 Rain (Pty) Ltd.
Contents
1 History
2 Television
3 Internet
4 Telecommunication landmarks
5 See also
6 References
7 External links
History[edit]
The first use of telecommunication in the Republic of South Africa was a single line telegraph connecting Cape Town and Simonstown[citation needed]. At about the time of the Bell Telephone Company's development of the telephone industry post-1876, early undersea telegraph links were introduced, first connecting Durban and Europe, and later connecting the country to the rest of the world[citation needed]. In the mid-twentieth century undersea telephone cables were also commissioned.
The network continued to develop through internal financing in a heavily regulated market as international technology developed. At this point, telephone services were operated by the South African Post Office. In the 1960s, South Africa was connected to 72 nations and total outgoing annual international calls numbered over 28,800[citation needed].
In the 1990s, South Africa launched a mobile operations, underwritten by Telkom in partnership with Vodafone. This subsidiary grew to be Vodacom, which Telkom sold in late 2008 in preference for its own 3G network[citation needed]. Vodacom has a subscriber base of more than R45M, with an ARPU of more than R60 across both rural and urban subscribers[citation needed]. Vodacom, together with the other operators, have come under criticism in late 2009 by government and the public for high interconnect charges.[3] This issue was currently being discussed by the Parliamentary Committee on Telecommunications[citation needed].
In 2004, the Department of Communications redefined the Electronics Communications Act, which consolidated and redefined the landscape of telecommunications licensing in South Africa (both mobile and fixed)[citation needed]. The Independent Communications Authority (ICASA) currently licenses more than 400 independent operators with the Electronic Communications Network License (with the ability to self-provision) as well as issuing Electronic Communications Service Licenses for service deployment over infrastructure in the retail domain[citation needed].
Telkom is no longer the single operator in South Africa, and faces competition from the second Fixed Network Operator Licensee, Neotel, as well as the four mobile operators, Vodacom, MTN, Cell-C[citation needed] and Rain. However, it still receives criticisms (see later) from smaller operators and the Competition Commission for setting South African broadband pricing in its favour[citation needed].
Television[edit]
Main article: Television in South Africa
Four main television stations are available to the public. These are namely SABC 1, SABC 2, SABC 3 and eTV[citation needed]. Other community-based stations are also on offer, such as Soweto TV and Cape Town TV (ctv).
DStv is currently South Africa's only operating and Africa's largest satellite television provider. The company provides over 100 video and over 78 audio channels, and in 2008 introduced its first HD video channel. Since then an additional five HD channels have been introduced - namely M-Net HD, SuperSport HD, Discovery HD, SuperSport HD 2, M-Net Movies 1 HD and SuperSport HD 3.[4]
In 2008, additional pay-TV licenses were granted to various companies in South Africa. As of January 2010, none of the companies granted a license have begun providing services. However, On Digital Media (ODM), have stated that they are on track to begin sale of their product in May 2010, and that prices will be significantly cheaper than their competitor DStv[citation needed]. In 2012, DSTV now has added 8 more channels all for movies.
Internet[edit]
Main article: Internet in South Africa
Although expensive compared to more developed nations, broadband is easily obtainable in South Africa. Fixed line options such as ADSL, ISDN, Diginet and Leased Lines are available from the national operator Telkom. Recently,[when?] legislation was passed by government allowing all licensed telecommunications providers to build their own fixed line networks, resulting in a scramble by companies such as Vodacom, MTN South Africa and Neotel to construct their own country and citywide fibre-optic networks. Individual South African cities such as Cape Town, Durban, Johannesburg and Pretoria are also in the process of, or have completed construction of city-owned fibre-optic networks. These will provide services to city and government-owned establishments, and will act as an extra source of income through the sale of excess bandwidth mainly to companies.
Wireless options are available from Sentech, iBurst, Vodacom, MTN, Cell C, Telkom and a number of other ISP's. They typically provide speeds of up to 7.6 Mbit/s with HSDPA. HSUPA is also available. MTN South Africa was among the very first mobile networks in the world to offer HSDPA services to its customers. Satellite options are available from both Sentech and Telkom.
A SNO, Neotel, has been licensed in South Africa and is currently offering a wireless service in selected areas. According to Neotel, up-take of its services has exceeded expectations, and as a result Neotel are rapidly expanding services throughout major metropolitan areas in South Africa. In 2009, SEACOM - the second undersea cable to land in South Africa - jointly owned and operated by Neotel - was switched on. Neotel have stated that sale of SEACOM bandwidth, too, has exceeded expectations, and will drive the continual downward-spiral of internet prices in the country. As of January 2010, South Africa has over 2 million broadband subscribers. Whilst this is the largest number in Africa, South Africa's broadband penetration of 4% is significantly below international standards.
Telecommunication landmarks[edit]
The first telephone patent was issued to Alexander Graham Bell in March 1876. The first use of telecommunication in the Union of South Africa was a single line telegraph connecting Cape Town and Simonstown. After Bell Labs' development of undersea telephone signal repeaters, the first undersea links were introduced connecting Durban and Europe, and soon after to the rest of the world. The network continued in a heavily regulated market as international technology developed. Until 1991 telephone services were operated by the South African Postal Service.
Telkom was incorporated on 30 September 1991 as a public limited liability company registered under the South African Companies Act, 61 of 1973, as amended.[5]
In 1993 GSM was demonstrated for the first time in Africa at Telkom '93 in Cape Town. In 1994 the first GSM networks in Africa were launched in South Africa.[6]
The first public videoconference between the continent of Africa and North America occurred on 24 June 1995 (2:00-3:00 p.m. PST). The Cybersafari Digital Be-In and Internet Love-Fest linked a technology fair at Fort Mason in San Francisco[7] with a techno "rave" and cyber-deli in Woodstock, Cape Town. For one hour, members of the public communicated with each other via a simple Picturetel system using a 128kb ISDN line. "Cognitive dissident" and communications activist David Robert Lewis initiated the video conference and peacecast[8] on the San Francisco side, and Freddie Bell answered the call in Woodstock, Cape Town. Because of different ISDN standards, a video bridge via Boston was used to achieve the link, which also featured interactive dancing. Organisations which took credit were technology sponsors Picturetel and Telkom, plus Peacecast organisors Unity 95, Parallel University, Vortex, Creativity Cafe and line producer "Cybersafari to Africa".
See also[edit]
Digital Divide in South Africa
Internet censorship in South Africa internetet
References[edit]
Jump up ^ "SA mobile subscribers in 2017: Vodacom vs MTN vs Cell C vs Telkom". Retrieved 2017-11-15.
Jump up ^ "Vodacom vs MTN vs Cell C vs Telkom – Mobile subscriber numbers". Retrieved 2017-11-15.
Jump up ^ Consumer Fair site Archived 20 May 2009 at the Wayback Machine.
Jump up ^ [1] DStv.com Channels
Jump up ^ "Telkom". Telkom. Retrieved 2018-08-01.
Jump up ^ History of GSM Archived 21 November 2010 at the Wayback Machine.
Jump up ^ "UNITY FOUNDATION - Events: 1990 through 1999". www.unityfoundation.org. Retrieved 2018-08-01.
Jump up ^ "KidCast Central; KidCast for Peace: Solutions for a Better World Homepage". creativity.net. Retrieved 2018-08-01.
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Tanya Bardsley
From Wikipedia, the free encyclopedia
Jump to: navigation, search
This biography of a living person needs additional citations for verification. Please help by adding reliable sources. Contentious material about living persons that is unsourced or poorly sourced must be removed immediately, especially if potentially libelous or harmful. (April 2017) (Learn how and when to remove this template message)
Tanya Bardsley
Born
Tanya Louise Robinson
(1981-04-29) 29 April 1981 (age 36)
Wigan, Greater Manchester, England
Spouse(s)
Phil Bardsley
Children
4
Modelling information
Height
5 ft 3 in (1.60 m)
Hair colour
Brown
Eye colour
Brown
Agency
United Agents
Tanya Louise Bardsley (née Robinson; born 29 April 1981) is an English model, born in Wigan, Greater Manchester, and grew up in Richmond, North Yorkshire. She is currently starring in the reality television series The Real Housewives of Cheshire. She is also the wife of footballer Phil Bardsley.
Biography[edit]
Robinson has appeared on the cover of Zoo Weekly, Ice, and several times in FHM magazine, as being the winner of their inaugural "High Street Honeys" competition in 2002,[1] and being named to their "100 Sexiest Women in the World" list in 2003 (38), 2004 (32), 2005 (41), 2006 (29) and 2007(63).[2]
In 2003, Robinson appeared in a Lynx advert where she appeared as a pizza delivery girl in pink underwear.[citation needed] In 2004, Robinson presented two programmes on Sky One called Gamenation and Strike every Friday night for a year. She also appeared in an episode of Celebrity Fear Factor, and had a small role in a French comedy film Double Zéro.[3]
Robinson had breast enlargement surgery going from a B cup to a 32D. In 2007, she appeared topless for the first time since getting her breasts enlarged in Zoo, having previously only been photographed topless on holiday before her breast enlargement.[4] Robinson has since posed topless in shoots for FHM and ZOO,[5][6] including a shoot for Zoo with fellow High Street Honey Kayleigh Pearson.
References[edit]
Jump up ^ "Internet Movie Database: Tanya Robinson". Retrieved 30 March 2006.
Jump up ^ "Archived copy". Archived from the original on 31 August 2009. Retrieved 21 August 2009.
Jump up ^ "French Spies". 16 June 2004 – via IMDb.
Jump up ^ "Man On - Facebook".
Jump up ^ Zoo Magazine 2008 "Golden Brown"
Jump up ^ Zoo Magazine 2008, Tanya Robinson Calendar 2009 Preview, Pages 48-52]
External links[edit]
Tanya Bardsley on IMDb
Retrieved from "https://en.wikipedia.org/w/index.php?title=Tanya_Bardsley&oldid=834401766"
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text:
New Zealand women's national cricket team
From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
New Zealand
White Ferns logo
Nickname(s)
White Ferns
Association
New Zealand Cricket
Personnel
Captain
Suzie Bates
Coach
Haidee Tiffen
International Cricket Council
ICC status
Full member (1926)
ICC region
East Asia-Pacific
ICC Rankings
Current [1] Best-ever
Women's
3rd 2nd
Women's Tests
First WTest
v England at Lancaster Park, Christchurch; 16–18 February 1935
Last WTest
v England at North Marine Road Ground, Scarborough; 21–24 August 2004
WTests
Played Won/Lost
Total [2]
45 2/10
(33 draws)
Women's One Day Internationals
First WODI
v Trinidad and Tobago at Clarence Park, St Albans; 23 June 1973
Last WODI
v Ireland at the Clontarf Cricket Club, Dublin; 13 June 2018
WODIs
Played Won/Lost
Total [4]
320 162/150
(2 ties, 6 no result)
This year [5]
0 0/0
(0 ties, 0 no result)
Women's World Cup Appearances
11 (first in 1973)
Best result
Champions (2000)
Women's Twenty20 Internationals
First WT20I
v England at the County Cricket Ground, Hove; 5 August 2004
Last WT20I
v Pakistan at the Sharjah Cricket Stadium, Sharjah; 14 November 2017
WT20Is
Played Won/Lost
Total [6]
96 57/36
(2 ties, 1 no result)
This year [7]
0 0/0
(0 ties, 0 no result)
Women's World Twenty20 Appearances
5 (first in 2009)
Best result
Runners-up (2009, 2010)
As of 8 July 2018
The New Zealand women's national cricket team, nicknamed the White Ferns, represents New Zealand in international women's cricket. One of eight teams competing in the ICC Women's Championship (the highest level of international women's cricket), the team is organised by New Zealand Cricket, a full member of the International Cricket Council (ICC).
New Zealand made its Test debut in 1935, against England, becoming the third team to play at that level. With Australia and England, New Zealand is one of only three teams to have participated in all ten editions of the Women's Cricket World Cup. The team has made the final of the tournament on four occasions, winning in 2000 and placing second in 1993, 1997, and 2009. At the Women's World Twenty20, New Zealand were runners-up in 2009 and 2010, but are yet to win the event.
Contents
1 Tournament history
1.1 World Cup
2 Current international rankings Top 10
3 Current squad
4 Coaching staff
5 Records
5.1 Test cricket
5.2 ODI cricket
6 See also
7 Notes
8 External links
Tournament history[edit]
World Cup[edit]
1973: 3rd place
1978: 3rd place
1982: 3rd place
1988: 3rd place
1993: Runners up
1997: Runners up
2000: Champions
2005: Semi Finals
2009: Runners up
2013: 4th place
2017: Group stage
Current international rankings Top 10[edit]
The ICC Women's Rankings incorporates results from Tests, ODIs and T20Is into a single ranking system.
ICC Women's Rankings
v
t
e
Rank
Team
Matches
Points
Rating
1
Australia 54 7,157 133
2
England 45 5,715 127
3
New Zealand 57 6,900 121
4
India 59 6,672 113
5
West Indies 48 4,725 98
6
South Africa 62 5,775 93
7
Pakistan 52 3,920 75
8
Sri Lanka 52 3,256 63
9
Bangladesh 19 704 37
10
Ireland 17 504 30
Reference: icc-cricket.com, espncricinfo.com, 31 March 2018
Current squad[edit]
Name
Age
Batting style
Bowling style
Domestic team
Forms
S／N
Captain, Opening Batswoman and All-rounder
Suzie Bates 30 Right-Handed Right-arm medium-fast Otago ODI, Twenty20 23
Vice Captain and All-Rounder
Sophie Devine 28 Right-handed Right-arm medium-fast Wellington ODI, Twenty20 77
Batswomen
Natalie Dodd 25 Right-handed Right-arm off break Northern Districts ODI, Twenty20
Maddy Green 25 Right-handed Right-arm off break Auckland ODI, Twenty20 51
Amy Satterthwaite 31 Left-handed Right-arm medium Canterbury ODI, Twenty20 17
Katie Perkins 30 Right-handed Right-arm medium Auckland ODI, Twenty20 70
Wicketkeepers
Rachel Priest 32 Right-handed N/A Wellington ODI, Twenty20 13
Sara McGlashan 36 Right-handed N/A Auckland ODI, Twenty20 28
Katey Martin 33 Right-handed N/A Otago ODI, Twenty20 15
All-rounders
Kate Ebrahim 26 Right-handed Right-arm medium Central Districts ODI, Twenty20
Leigh Kasperek 23 Right-handed Right-arm off break Otago ODI, Twenty20 62
Anna Peterson 27 Right-handed Right-arm medium Auckland ODI, Twenty20 52
Pace Bowlers
Lea Tahuhu 27 Right-handed Right-arm medium-fast Canterbury ODI, Twenty20 6
Hannah Rowe 21 Right-handed Right-arm medium Central Districts ODI, Twenty20 74
Holly Huddleston 30 Right-handed Right-arm medium Auckland ODI, Twenty20 74
Thamsyn Newton 20 Right-handed Right-arm medium Canterbury Twenty20 99
Felicity Leydon-Davis 20 Right-handed Right-arm medium Northern Districts Twenty20 49
Spin Bowlers
Georgia Guy 24 Right-handed Right-arm Off break Auckland ODI, Twenty20
Erin Bermingham 27 Right-handed Leg break Canterbury ODI, Twenty20 19
Morna Nielsen 28 Right-handed Slow left-arm orthodox Otago ODI, Twenty20 54
Amelia Kerr 17 Right-handed Right-arm leg break Wellington ODI, Twenty20 48
Coaching staff[edit]
Head Coach: Haidee Tiffen
Assistant Coach: Matthew Bell
Team's Manager: Helen Mahon-Stroud
Physiotherapist: Helen Littleworth
Records[edit]
Test cricket[edit]
As of August 2017[update]:
Most Test runs for New Zealand[8]
Player
Runs
Average
Debbie Hockley 1,301 52.04
Judi Doull 779 43.27
Trish McKelvey 699 29.12
Jackie Clark 482 26.77
Kirsty Bond 473 67.57
Most Test wickets for New Zealand[9]
Player
Wickets
Average
Jackie Lord 55 19.07
Jill Saulbrey 35 27.17
Pat Carrick 21 23.28
Jos Burley 21 26.33
Jean Coulston 19 17.94
Highest team total: 517/8 v England, 24 June 1996 at North Marine Road Ground, Scarborough, England
Highest individual innings: 204, Kirsty Flavell v England, 24 June 1996 at North Marine Road Ground, Scarborough, England
Best innings bowling: 7/41, Jos Burley v England, 6 August 1966 at The Oval, London, England
Best match bowling: 10/137, Jackie Lord v Australia, 26 January 1979 at Melbourne, Australia
ODI cricket[edit]
As of July 2018[update]:
Most One-Day International runs for New Zealand[10]
Player
Runs
Average
Debbie Hockley 4,064 41.89
Suzie Bates 3,734 42.43
Amy Satterthwaite 3,168 38.63
Haidee Tiffen 2,919 30.72
Emily Drumm 2,844 35.11
Most One-Day International wickets for New Zealand[11]
Player
Wickets
Average
Aimee Watkins 92 31.04
Nicola Browne 88 34.14
Catherine Campbell 78 25.87
Rachel Pullar 88 34.14
Suzie Bates 73 32.56
Highest team total: 490/4 v Ireland, 8 June 2018 at Dublin, Ireland
Highest individual innings: 232 not out, Amelia Kerr v Ireland, 13 June 2018 at YMCA Cricket Club, Dublin, Republic of Ireland
Best innings bowling: 6/10, Jackie Lord v India, 14 January 1982 at Auckland, New Zealand
See also[edit]
New Zealand men's team
Notes[edit]
Jump up ^ "ICC Rankings". icc-cricket.com.
Jump up ^ "Women's Test matches - Team records". ESPNcricinfo.
Jump up ^ "Women's Test matches - 2018 Team records". ESPNcricinfo.
Jump up ^ "WODI matches - Team records". ESPNcricinfo.
Jump up ^ "WODI matches - 2018 Team records". ESPNcricinfo.
Jump up ^ "WT20I matches - Team records". ESPNcricinfo.
Jump up ^ "WT20I matches - 2018 Team records". ESPNcricinfo.
Jump up ^ "New Zealand Women / Records / Women's Test matches / Most runs". ESPN Cricinfo. Retrieved August 14, 2017.
Jump up ^ "New Zealand Women / Records / Women's Test matches / Most wickets". ESPN Cricinfo. Retrieved August 14, 2017.
Jump up ^ "New Zealand Women / Records / Women's One-Day Internationals / Most runs". ESPN Cricinfo. Retrieved August 14, 2017.
Jump up ^ "New Zealand Women / Records / Women's One-Day International matches / Most wickets". ESPN Cricinfo. Retrieved August 14, 2017.
External links[edit]
official website
show
v
t
e
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Governing body
New Zealand Cricket
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U-19
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show
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Retrieved from "https://en.wikipedia.org/w/index.php?title=New_Zealand_women%27s_national_cricket_team&oldid=851695009"
Categories:
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Women's One Day International

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Roller Derby Team New Zealand

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