The Experts below are selected from a list of 267 Experts worldwide ranked by ideXlab platform
Ryan J. Tibshirani - One of the best experts on this subject based on the ideXlab platform.
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a higher order kolmogorov smirnov test
International Conference on Artificial Intelligence and Statistics, 2019Co-Authors: Veeranjaneyulu Sadhanala, Aaditya Ramdas, Yu-xiang Wang, Ryan J. TibshiraniAbstract:We present an extension of the Kolmogorov-Smirnov (KS) two-sample test, which can be more sensitive to differences in the tails. Our test statistic is an integral probability metric (IPM) defined over a higher-order total variation ball, recovering the original KS test as its simplest case. We give an exact representer result for our IPM, which generalizes the fact that the original KS test statistic can be expressed in equivalent variational and CDF forms. For small enough orders (k <= 5), we develop a linear-time algorithm for computing our higher-order KS test statistic; for all others (k >= 6), we give a nearly linear-time approximation. We derive the asymptotic null distribution for our test, and show that our nearly linear-time approximation shares the same asymptotic null. Lastly, we complement our theory with numerical studies.
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A Higher-Order Kolmogorov-Smirnov Test
arXiv: Machine Learning, 2019Co-Authors: Veeranjaneyulu Sadhanala, Aaditya Ramdas, Yu-xiang Wang, Ryan J. TibshiraniAbstract:We present an extension of the Kolmogorov-Smirnov (KS) two-sample test, which can be more sensitive to differences in the tails. Our test statistic is an integral probability metric (IPM) defined over a higher-order total variation ball, recovering the original KS test as its simplest case. We give an exact representer result for our IPM, which generalizes the fact that the original KS test statistic can be expressed in equivalent variational and CDF forms. For small enough orders ($k \leq 5$), we develop a linear-time algorithm for computing our higher-order KS test statistic; for all others ($k \geq 6$), we give a nearly linear-time approximation. We derive the asymptotic null distribution for our test, and show that our nearly linear-time approximation shares the same asymptotic null. Lastly, we complement our theory with numerical studies.
Harry J. Khamis - One of the best experts on this subject based on the ideXlab platform.
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The two-stage i -corrected Kolmogorov-Smirnov test
Journal of Applied Statistics, 2000Co-Authors: Harry J. KhamisAbstract:The delta-corrected Kolmogorov-Smirnov test has been shown to be uniformly more powerful than the classical Kolmogorov-Smirnov test for small to moderate sample sizes. However, the delta-corrected test consists of two tests, leading to a slight inflation of the experimentwise type I error rate. The critical values of the delta-corrected test are adjusted to take into account the two-stage nature of the test, ensuring an experimentwise error rate at the nominal level. A power study confirms that the resulting so-called two-stage delta-corrected test is uniformly more powerful than the classical Kolmogorov-Smirnov test, with power improvements of up to 46 percentage points.
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The Two-Stage Delta-Corrected Kolmogorov-Smirnov Test
Journal of Applied Statistics, 2000Co-Authors: Harry J. KhamisAbstract:Abstract The delta-corrected Kolmogorov-Smirnov test has been shown to be uniformly more powerful than the classical Kolmogorov-Smirnov test for small to moderate sample sizes. However, the delta-corrected test consists of two tests, leading to a slight inflation of the experimentwise type I error rate. The critical values of the delta-corrected test are adjusted to take into account the two-stage nature of the test, ensuring an experimentwise error rate at the nominal level. A power study confirms that the resulting so-called two-stage delta-corrected test is uniformly more powerful than the classical Kolmogorov-Smirnov test, with power improvements of up to 46 percentage points.
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The delta-corrected Kolmogorov-Smirnov test for the two-parameter Weibull distribution
Journal of Applied Statistics, 1997Co-Authors: Harry J. KhamisAbstract:Monte Carlo simulation techniques are used to create tables of critical values for the delta-corrected Kolmogorov-Smirnov statistic-a modification of the classical Kolmogorov-Smirnov statistic-for the Weibull distribution with known location parameter and unknown shape and scale parameters. The power of the proposed test is investigated relative to values of delta in the unit interval and relative to a wide variety of alternative distributions. The results indicate that using the delta-correction can lead to as many as 8.4 percentage points more power than can be achieved with the classical Kolmogorov-Smirnov test, with no change in the size of the test. Furthermore, carrying out the delta-corrected test involves no more steps or calculations than for the classical Kolmogorov-Smirnov test. In general, it is shown that a slight modification-or correction-in the definition of the empirical distribution function of the Kolmogorov-Smirnov test can lead to power enhancement without changing the type I error rate of the test. Two examples clearly show the effectiveness of the delta-corrected test. The delta-corrected Kolmogorov-Smirnov test is recommended for testing the goodness of fit to the twoparameter Weibull distribution.
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The Delta-Corrected Kolmogorov-Smirnov Test for the Two-Parameter Weibull Distribution
Journal of Applied Statistics, 1997Co-Authors: Harry J. KhamisAbstract:Summary Monte Carlo simulation techniques are used to create tables of critical values for the delta-corrected Kolmogorov-Smirnov statistic-a modification of the classical Kolmogorov-Smirnov statistic-for the Weibull distribution with known location parameter and unknown shape and scale parameters. The power of the proposed test is investigated relative to values of delta in the unit interval and relative to a wide variety of alternative distributions. The results indicate that using the delta-correction can lead to as many as 8.4 percentage points more power than can be achieved with the classical Kolmogorov-Smirnov test, with no change in the size of the test. Furthermore, carrying out the delta-corrected test involves no more steps or calculations than for the classical Kolmogorov-Smirnov test. In general, it is shown that a slight modification-or correction-in the definition of the empirical distribution function of the Kolmogorov-Smirnov test can lead to power enhancement without changing the type I ...
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A Comparative Study of the Delta-Corrected Kolmogorov-Smirnov Test
Journal of Applied Statistics, 1993Co-Authors: Harry J. KhamisAbstract:The delta-corrected Kolmogorov-Smirnov test has been shown to be uniformly more powerful than the classical Kolmogorov-Smirnov test. The power of the delta-corrected Kolmogorov-Smimov test is compa...
Rand R. Wilcox - One of the best experts on this subject based on the ideXlab platform.
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Encyclopedia of Biostatistics - Kolmogorov–Smirnov Test
Encyclopedia of Biostatistics, 2005Co-Authors: Rand R. WilcoxAbstract:This is a distribution-free method for comparing two empirical distributions, based on the largest vertical distance between the two cumulative distribution functions. The Kolmogorov test is a special case where one distribution function is known, and hence is a test of goodness-of-fit. Various properties, including power, are discussed. Keywords: distribution-free; nonparametric; goodness-of-fit; power; quantile; distribution function
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kolmogorov smirnov test
Encyclopedia of Biostatistics, 2005Co-Authors: Rand R. WilcoxAbstract:This is a distribution-free method for comparing two empirical distributions, based on the largest vertical distance between the two cumulative distribution functions. The Kolmogorov test is a special case where one distribution function is known, and hence is a test of goodness-of-fit. Various properties, including power, are discussed. Keywords: distribution-free; nonparametric; goodness-of-fit; power; quantile; distribution function
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Some practical reasons for reconsidering the Kolmogorov‐Smirnov test
British Journal of Mathematical and Statistical Psychology, 1997Co-Authors: Rand R. WilcoxAbstract:The Kolmogorov-Smirnov test is a method for comparing the distributions of two independent groups that has virtually disappeared from applied research and introductory statistics books for the social sciences. The apparent reason is the perception that it has low power compared to methods for comparing means in particular and measures of location in general. However, extant studies comparing the power of the Kolmogorov-Smirnov test to other methods for comparing means are limited to normal distributions having a common variance. This note points out that, even under a shift model, the Kolmogorov-Smirnov test not only can have high power relative to methods for comparing robust measures of location, there are situations where it has higher power than methods for comparing robust measurement of location. Some additional features of the Kolmogorov-Smirnov test are noted, and a simple S-PLUS program for computing the exact significance level is provided. Data from a study on the effects of drinking alcohol are used to illustrate the potential advantage of the Kolmogorov-Smirnov test.
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some practical reasons for reconsidering the kolmogorov smirnov test
British Journal of Mathematical and Statistical Psychology, 1997Co-Authors: Rand R. WilcoxAbstract:The Kolmogorov-Smirnov test is a method for comparing the distributions of two independent groups that has virtually disappeared from applied research and introductory statistics books for the social sciences. The apparent reason is the perception that it has low power compared to methods for comparing means in particular and measures of location in general. However, extant studies comparing the power of the Kolmogorov-Smirnov test to other methods for comparing means are limited to normal distributions having a common variance. This note points out that, even under a shift model, the Kolmogorov-Smirnov test not only can have high power relative to methods for comparing robust measures of location, there are situations where it has higher power than methods for comparing robust measurement of location. Some additional features of the Kolmogorov-Smirnov test are noted, and a simple S-PLUS program for computing the exact significance level is provided. Data from a study on the effects of drinking alcohol are used to illustrate the potential advantage of the Kolmogorov-Smirnov test.
Veeranjaneyulu Sadhanala - One of the best experts on this subject based on the ideXlab platform.
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a higher order kolmogorov smirnov test
International Conference on Artificial Intelligence and Statistics, 2019Co-Authors: Veeranjaneyulu Sadhanala, Aaditya Ramdas, Yu-xiang Wang, Ryan J. TibshiraniAbstract:We present an extension of the Kolmogorov-Smirnov (KS) two-sample test, which can be more sensitive to differences in the tails. Our test statistic is an integral probability metric (IPM) defined over a higher-order total variation ball, recovering the original KS test as its simplest case. We give an exact representer result for our IPM, which generalizes the fact that the original KS test statistic can be expressed in equivalent variational and CDF forms. For small enough orders (k <= 5), we develop a linear-time algorithm for computing our higher-order KS test statistic; for all others (k >= 6), we give a nearly linear-time approximation. We derive the asymptotic null distribution for our test, and show that our nearly linear-time approximation shares the same asymptotic null. Lastly, we complement our theory with numerical studies.
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A Higher-Order Kolmogorov-Smirnov Test
arXiv: Machine Learning, 2019Co-Authors: Veeranjaneyulu Sadhanala, Aaditya Ramdas, Yu-xiang Wang, Ryan J. TibshiraniAbstract:We present an extension of the Kolmogorov-Smirnov (KS) two-sample test, which can be more sensitive to differences in the tails. Our test statistic is an integral probability metric (IPM) defined over a higher-order total variation ball, recovering the original KS test as its simplest case. We give an exact representer result for our IPM, which generalizes the fact that the original KS test statistic can be expressed in equivalent variational and CDF forms. For small enough orders ($k \leq 5$), we develop a linear-time algorithm for computing our higher-order KS test statistic; for all others ($k \geq 6$), we give a nearly linear-time approximation. We derive the asymptotic null distribution for our test, and show that our nearly linear-time approximation shares the same asymptotic null. Lastly, we complement our theory with numerical studies.
Yu-xiang Wang - One of the best experts on this subject based on the ideXlab platform.
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a higher order kolmogorov smirnov test
International Conference on Artificial Intelligence and Statistics, 2019Co-Authors: Veeranjaneyulu Sadhanala, Aaditya Ramdas, Yu-xiang Wang, Ryan J. TibshiraniAbstract:We present an extension of the Kolmogorov-Smirnov (KS) two-sample test, which can be more sensitive to differences in the tails. Our test statistic is an integral probability metric (IPM) defined over a higher-order total variation ball, recovering the original KS test as its simplest case. We give an exact representer result for our IPM, which generalizes the fact that the original KS test statistic can be expressed in equivalent variational and CDF forms. For small enough orders (k <= 5), we develop a linear-time algorithm for computing our higher-order KS test statistic; for all others (k >= 6), we give a nearly linear-time approximation. We derive the asymptotic null distribution for our test, and show that our nearly linear-time approximation shares the same asymptotic null. Lastly, we complement our theory with numerical studies.
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A Higher-Order Kolmogorov-Smirnov Test
arXiv: Machine Learning, 2019Co-Authors: Veeranjaneyulu Sadhanala, Aaditya Ramdas, Yu-xiang Wang, Ryan J. TibshiraniAbstract:We present an extension of the Kolmogorov-Smirnov (KS) two-sample test, which can be more sensitive to differences in the tails. Our test statistic is an integral probability metric (IPM) defined over a higher-order total variation ball, recovering the original KS test as its simplest case. We give an exact representer result for our IPM, which generalizes the fact that the original KS test statistic can be expressed in equivalent variational and CDF forms. For small enough orders ($k \leq 5$), we develop a linear-time algorithm for computing our higher-order KS test statistic; for all others ($k \geq 6$), we give a nearly linear-time approximation. We derive the asymptotic null distribution for our test, and show that our nearly linear-time approximation shares the same asymptotic null. Lastly, we complement our theory with numerical studies.
