Kernels Based Tests with Non-Asymptotic Bootstrap Approaches for Two-Sample Problems
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
Text
Fromont et al. "Kernels Based Tests with Non-Asymptotic Bootstrap Approaches for Two-Sample Problems." Proceedings of the 25th Annual Conference on Learning Theory, 2012.Markdown
[Fromont et al. "Kernels Based Tests with Non-Asymptotic Bootstrap Approaches for Two-Sample Problems." Proceedings of the 25th Annual Conference on Learning Theory, 2012.](https://mlanthology.org/colt/2012/fromont2012colt-kernels/)BibTeX
@inproceedings{fromont2012colt-kernels,
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},
year = {2012},
pages = {23.1-23.23},
volume = {23},
url = {https://mlanthology.org/colt/2012/fromont2012colt-kernels/}
}