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Reports (Research Report) Year : 2015

A Sequential Nonparametric Two-Sample Test

Un Test Non-paramétrique d'Homogénéité Séquentiel

Alix Lhéritier
Frédéric Cazals

Abstract

Given samples from two distributions, a nonparametric two-sample test aims at determining whether the two distributions are equal or not, based on a test statistic. This statistic may be computed on the whole dataset, or may be computed on a subset of the dataset by a function trained on its complement. We propose a third tier, consisting of functions exploiting a sequential framework to learn the differences while incrementally processing the data. Sequential processing naturally allows optional stopping, which makes our test the first truly sequential nonparametric two-sample test. We show that any sequential predictor can be turned into a sequential two-sample test for which a valid $p$-value can be computed, yielding controlled type I error. We also show that pointwise universal predictors yield consistent tests, which can be built with a nonparametric regressor based on $k$-nearest neighbors in particular. We also show that mixtures and switch distributions can be used to increase power, while keeping consistency.
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Dates and versions

hal-01135608 , version 1 (25-03-2015)
hal-01135608 , version 2 (02-06-2015)

Identifiers

  • HAL Id : hal-01135608 , version 2

Cite

Alix Lhéritier, Frédéric Cazals. A Sequential Nonparametric Two-Sample Test. [Research Report] RR-8704, Inria. 2015, pp.18. ⟨hal-01135608v2⟩
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