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Permutation tests for equality of distributions in high-dimensional settings

Hall, P and Tajvidi, Nader LU (2002) In Biometrika 89(2). p.359-374
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... (More)
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. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
rank test, resampling, multivariate analysis, local alternative, hypothesis test, hypergeometric distribution, bootstrap, functional data analysis
in
Biometrika
volume
89
issue
2
pages
359 - 374
publisher
Biometrika Trust
external identifiers
  • wos:000176520500008
  • scopus:22944460361
ISSN
0006-3444
DOI
10.1093/biomet/89.2.359
language
English
LU publication?
yes
id
2ce5c9ac-b70a-47cd-9695-2814e5c08d6d (old id 334616)
date added to LUP
2007-08-23 09:23:16
date last changed
2017-11-19 04:05:26
@article{2ce5c9ac-b70a-47cd-9695-2814e5c08d6d,
  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.},
  author       = {Hall, P and Tajvidi, Nader},
  issn         = {0006-3444},
  keyword      = {rank test,resampling,multivariate analysis,local alternative,hypothesis test,hypergeometric distribution,bootstrap,functional data analysis},
  language     = {eng},
  number       = {2},
  pages        = {359--374},
  publisher    = {Biometrika Trust},
  series       = {Biometrika},
  title        = {Permutation tests for equality of distributions in high-dimensional settings},
  url          = {http://dx.doi.org/10.1093/biomet/89.2.359},
  volume       = {89},
  year         = {2002},
}