Permutation tests for equality of distributions in high-dimensional settings

Research output: Contribution to journalArticle

Abstract

Motivated by applications in high-dimensional settings, we suggest a test of the hypothesis H-0 that two sampled distributions are identical. It is assumed that two independent datasets are drawn from the respective populations, which may be very general. In particular, the distributions may be multivariate or infinite-dimensional, in the latter case representing, for example, the distributions of random functions from one Euclidean space to another. Our test uses a measure of distance between data. This measure should be symmetric but need not satisfy the triangle inequality, so it is not essential that it be a metric. The test is based on ranking the pooled dataset, with respect to the distance and relative to any fixed data value, and repeating this operation for each fixed datum. A permutation argument enables a critical point to be chosen such that the test has concisely known significance level, conditional on the set of all pairwise distances.

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Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Probability Theory and Statistics

Keywords

  • rank test, resampling, multivariate analysis, local alternative, hypothesis test, hypergeometric distribution, bootstrap, functional data analysis
Original languageEnglish
Pages (from-to)359-374
JournalBiometrika
Volume89
Issue number2
Publication statusPublished - 2002
Publication categoryResearch
Peer-reviewedYes