Kernels based tests with non-asymptotic bootstrap approaches for two-sample problem

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.
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Communication dans un congrès
Shie Mannor, Nathan Srebro, Robert C. Williamson. 25th Annual Conference on Learning Theory, Jun 2012, Edimbourg, United Kingdom. 23, pp.23.1-23.22
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  • HAL Id : hal-00913879, version 1

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Magalie Fromont, Béatrice Laurent, Matthieu Lerasle, Patricia Reynaud-Bouret. Kernels based tests with non-asymptotic bootstrap approaches for two-sample problem. Shie Mannor, Nathan Srebro, Robert C. Williamson. 25th Annual Conference on Learning Theory, Jun 2012, Edimbourg, United Kingdom. 23, pp.23.1-23.22. <hal-00913879>

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