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Bounds for the chi-square approximation of Friedman's statistic by Stein's method

Abstract:

Friedman's chi-square test is a non-parametric statistical test for r≥2 treatments across n≥1 trials to assess the null hypothesis that there is no treatment effect. We use Stein's method with an exchangeable pair coupling to derive an explicit bound on the distance between the distribution of Friedman's statistic and its limiting chi-square distribution, measured using smooth test functions. Our bound is of the optimal order n−1, and also has an optimal dependence on the parameter r, in that...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.3150/22-BEJ1530

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Statistics
Role:
Author
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Name:
Engineering & Physical Sciences Research Council
Grant:
EP/K032402/1
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Name:
Engineering and Physical Sciences Research Council
Grant:
EP/R018472/1
Publisher:
Bernoulli Society for Mathematical Statistics and Probability
Journal:
Bernoulli - Journal of the Bernoulli Society More from this journal
Volume:
29
Issue:
3
Pages:
2008-2034
Publication date:
2023-04-27
Acceptance date:
2022-07-07
DOI:
ISSN:
1350-7265
Language:
English
Keywords:
Pubs id:
1266744
Local pid:
pubs:1266744
Deposit date:
2022-07-07

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