Permutation tests for equality of distributions in high-dimensional settings

Peter Hall*, Nader Tajvidi

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    95 Citations (Scopus)

    Abstract

    Motivated by applications in high-dimensional settings, we suggest a test of the hypothesis H0 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.

    Original languageEnglish
    Pages (from-to)359-374
    Number of pages16
    JournalBiometrika
    Volume89
    Issue number2
    DOIs
    Publication statusPublished - 2002

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