Two-sample homogeneity tests based on divergence measures

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• 作者：Max Wornowizki ; Roland Fried
• 关键词：Nonparametric two ; sample test ; Semiparametric two ; sample test ; Density ratio estimation ; Kullback ; Leibler divergence ; Hellinger distance ; Permutation test
• 刊名：Computational Statistics
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：31
• 期：1
• 页码：291-313
• 全文大小：596 KB
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• 作者单位：Max Wornowizki (1)
  Roland Fried (1)
  
  1. Department of Statistics, Technische Universität Dortmund, 44221, Dortmund, Germany
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Statistics
  Statistics
  Probability and Statistics in Computer Science
  Probability Theory and Stochastic Processes
  Economic Theory
  
• 出版者：Physica Verlag, An Imprint of Springer-Verlag GmbH
• ISSN：1613-9658

文摘

The concept of f-divergences introduced by Ali and Silvey (J R Stat Soc (B) 28:131–142, 1996) provides a rich set of distance like measures between pairs of distributions. Divergences do not focus on certain moments of random variables, but rather consider discrepancies between the corresponding probability density functions. Thus, two-sample tests based on these measures can detect arbitrary alternatives when testing the equality of the distributions. We treat the problem of divergence estimation as well as the subsequent testing for the homogeneity of two-samples. In particular, we propose a nonparametric estimator for f-divergences in the case of continuous distributions, which is based on kernel density estimation and spline smoothing. As we show in extensive simulations, the new method performs stable and quite well in comparison to several existing non- and semiparametric divergence estimators. Furthermore, we tackle the two-sample homogeneity problem using permutation tests based on various divergence estimators. The methods are compared to an asymptotic divergence test as well as to several traditional parametric and nonparametric procedures under different distributional assumptions and alternatives in simulations. It turns out that divergence based methods detect discrepancies between distributions more often than traditional methods if the distributions do not differ in location only. The findings are illustrated on ion mobility spectrometry data.