On a projective ensemble approach to two sample test for equality of distributions

Zhimei Li, Yaowu Zhang
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:6020-6027, 2020.

Abstract

In this work, we propose a robust test for the multivariate two-sample problem through projective ensemble, which is a generalization of the Cramer-von Mises statistic. The proposed test statistic has a simple closed-form expression without any tuning parameters involved, it is easy to implement can be computed in quadratic time. Moreover, our test is insensitive to the dimension and consistent against all fixed alternatives, it does not require the moment assumption and is robust to the presence of outliers. We study the asymptotic behaviors of the test statistic under the null and two kinds of alternative hypotheses. We also suggest a permutation procedure to approximate critical values and employ its consistency. We demonstrate the effectiveness of our test through extensive simulation studies and a real data application.

Cite this Paper


BibTeX
@InProceedings{pmlr-v119-li20s, title = {On a projective ensemble approach to two sample test for equality of distributions}, author = {Li, Zhimei and Zhang, Yaowu}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {6020--6027}, year = {2020}, editor = {Hal Daumé III and Aarti Singh}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/li20s/li20s.pdf}, url = { http://proceedings.mlr.press/v119/li20s.html }, abstract = {In this work, we propose a robust test for the multivariate two-sample problem through projective ensemble, which is a generalization of the Cramer-von Mises statistic. The proposed test statistic has a simple closed-form expression without any tuning parameters involved, it is easy to implement can be computed in quadratic time. Moreover, our test is insensitive to the dimension and consistent against all fixed alternatives, it does not require the moment assumption and is robust to the presence of outliers. We study the asymptotic behaviors of the test statistic under the null and two kinds of alternative hypotheses. We also suggest a permutation procedure to approximate critical values and employ its consistency. We demonstrate the effectiveness of our test through extensive simulation studies and a real data application.} }
Endnote
%0 Conference Paper %T On a projective ensemble approach to two sample test for equality of distributions %A Zhimei Li %A Yaowu Zhang %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-li20s %I PMLR %P 6020--6027 %U http://proceedings.mlr.press/v119/li20s.html %V 119 %X In this work, we propose a robust test for the multivariate two-sample problem through projective ensemble, which is a generalization of the Cramer-von Mises statistic. The proposed test statistic has a simple closed-form expression without any tuning parameters involved, it is easy to implement can be computed in quadratic time. Moreover, our test is insensitive to the dimension and consistent against all fixed alternatives, it does not require the moment assumption and is robust to the presence of outliers. We study the asymptotic behaviors of the test statistic under the null and two kinds of alternative hypotheses. We also suggest a permutation procedure to approximate critical values and employ its consistency. We demonstrate the effectiveness of our test through extensive simulation studies and a real data application.
APA
Li, Z. & Zhang, Y.. (2020). On a projective ensemble approach to two sample test for equality of distributions. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:6020-6027 Available from http://proceedings.mlr.press/v119/li20s.html .

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