Kernels Based Tests with Non-asymptotic Bootstrap Approaches for Two-sample Problems

Magalie Fromont, Béatrice Laurent, Matthieu Lerasle, Patricia Reynaud-Bouret
Proceedings of the 25th Annual Conference on Learning Theory, PMLR 23:23.1-23.23, 2012.

Abstract

Considering either two independent i.i.d. samples, or two independent samples generated from a heteroscedastic regression model, or two independent Poisson processes, we address the question of testing equality of their respective distributions. We first propose single testing procedures based on a general symmetric kernel. The corresponding critical values are chosen from a wild or permutation bootstrap approach, and the obtained tests are exactly (and not just asymptotically) of level. We then introduce an aggregation method, which enables to overcome the difficulty of choosing a kernel and/or the parameters of the kernel. We derive non-asymptotic properties for the aggregated tests, proving that they may be optimal in a classical statistical sense.

Cite this Paper

BibTeX
@InProceedings{pmlr-v23-fromont12, title = {Kernels Based Tests with Non-asymptotic Bootstrap Approaches for Two-sample Problems}, author = {Fromont, Magalie and Laurent, Béatrice and Lerasle, Matthieu and Reynaud-Bouret, Patricia}, booktitle = {Proceedings of the 25th Annual Conference on Learning Theory}, pages = {23.1--23.23}, year = {2012}, editor = {Mannor, Shie and Srebro, Nathan and Williamson, Robert C.}, volume = {23}, series = {Proceedings of Machine Learning Research}, address = {Edinburgh, Scotland}, month = {25--27 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v23/fromont12/fromont12.pdf}, url = {https://proceedings.mlr.press/v23/fromont12.html}, abstract = {Considering either two independent i.i.d. samples, or two independent samples generated from a heteroscedastic regression model, or two independent Poisson processes, we address the question of testing equality of their respective distributions. We first propose single testing procedures based on a general symmetric kernel. The corresponding critical values are chosen from a wild or permutation bootstrap approach, and the obtained tests are exactly (and not just asymptotically) of level. We then introduce an aggregation method, which enables to overcome the difficulty of choosing a kernel and/or the parameters of the kernel. We derive non-asymptotic properties for the aggregated tests, proving that they may be optimal in a classical statistical sense.} }
Endnote
%0 Conference Paper %T Kernels Based Tests with Non-asymptotic Bootstrap Approaches for Two-sample Problems %A Magalie Fromont %A Béatrice Laurent %A Matthieu Lerasle %A Patricia Reynaud-Bouret %B Proceedings of the 25th Annual Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2012 %E Shie Mannor %E Nathan Srebro %E Robert C. Williamson %F pmlr-v23-fromont12 %I PMLR %P 23.1--23.23 %U https://proceedings.mlr.press/v23/fromont12.html %V 23 %X Considering either two independent i.i.d. samples, or two independent samples generated from a heteroscedastic regression model, or two independent Poisson processes, we address the question of testing equality of their respective distributions. We first propose single testing procedures based on a general symmetric kernel. The corresponding critical values are chosen from a wild or permutation bootstrap approach, and the obtained tests are exactly (and not just asymptotically) of level. We then introduce an aggregation method, which enables to overcome the difficulty of choosing a kernel and/or the parameters of the kernel. We derive non-asymptotic properties for the aggregated tests, proving that they may be optimal in a classical statistical sense.
RIS
TY - CPAPER TI - Kernels Based Tests with Non-asymptotic Bootstrap Approaches for Two-sample Problems AU - Magalie Fromont AU - Béatrice Laurent AU - Matthieu Lerasle AU - Patricia Reynaud-Bouret BT - Proceedings of the 25th Annual Conference on Learning Theory DA - 2012/06/16 ED - Shie Mannor ED - Nathan Srebro ED - Robert C. Williamson ID - pmlr-v23-fromont12 PB - PMLR DP - Proceedings of Machine Learning Research VL - 23 SP - 23.1 EP - 23.23 L1 - http://proceedings.mlr.press/v23/fromont12/fromont12.pdf UR - https://proceedings.mlr.press/v23/fromont12.html AB - Considering either two independent i.i.d. samples, or two independent samples generated from a heteroscedastic regression model, or two independent Poisson processes, we address the question of testing equality of their respective distributions. We first propose single testing procedures based on a general symmetric kernel. The corresponding critical values are chosen from a wild or permutation bootstrap approach, and the obtained tests are exactly (and not just asymptotically) of level. We then introduce an aggregation method, which enables to overcome the difficulty of choosing a kernel and/or the parameters of the kernel. We derive non-asymptotic properties for the aggregated tests, proving that they may be optimal in a classical statistical sense. ER -
APA
Fromont, M., Laurent, B., Lerasle, M. & Reynaud-Bouret, P.. (2012). Kernels Based Tests with Non-asymptotic Bootstrap Approaches for Two-sample Problems. Proceedings of the 25th Annual Conference on Learning Theory, in Proceedings of Machine Learning Research 23:23.1-23.23 Available from https://proceedings.mlr.press/v23/fromont12.html.

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