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The permutation distribution of matrix correlation statistics


Barbour, A D; Chen, L H Y (2005). The permutation distribution of matrix correlation statistics. In: Barbour, A D; Chen, L H Y. Stein‘s method and applications. Singapore: World Scientific Publishing, 223-245.

Abstract

Many statistics used to test for association between pairs (yi, zi) of multivariate observations, sampled from n individuals in a population, are based on comparing the similarity aij of each pair (i, j) of individuals, as evidenced by the values yi and yj, with their similarity bij based on the values zi, and Zj. A common strategy is to compute the sample correlation between these two sets of values. The appropriate null hypothesis distribution is that derived by permuting the zi's at random among the individuals, while keeping the yi's fixed. In this paper, a Berry–Esseen bound for the normal approximation to this null distribution is derived, which is useful even when the matrices a and b are relatively sparse, as is the case in many applications. The proofs are based on constructing a suitable exchangeable pair, a technique at the heart of Stein's method.

Many statistics used to test for association between pairs (yi, zi) of multivariate observations, sampled from n individuals in a population, are based on comparing the similarity aij of each pair (i, j) of individuals, as evidenced by the values yi and yj, with their similarity bij based on the values zi, and Zj. A common strategy is to compute the sample correlation between these two sets of values. The appropriate null hypothesis distribution is that derived by permuting the zi's at random among the individuals, while keeping the yi's fixed. In this paper, a Berry–Esseen bound for the normal approximation to this null distribution is derived, which is useful even when the matrices a and b are relatively sparse, as is the case in many applications. The proofs are based on constructing a suitable exchangeable pair, a technique at the heart of Stein's method.

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Additional indexing

Item Type:Book Section, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2005
Deposited On:02 Feb 2010 19:16
Last Modified:05 Apr 2016 13:24
Publisher:World Scientific Publishing
Series Name:Lecture Notes Series. Institute for Mathematical Sciences. National University of Singapore.
Number:5
ISSN:1793-0758
ISBN:981-256-281-8
Additional Information:Electronic version of an article published as Lecture Notes Series. Institute for Mathematical Sciences. National University of Singapore, 5. Published jointly by Singapore University Press, Singapore; and World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005. xx+297 pp © 2005 copyright World Scientific Publishing Company http://www.worldscibooks.com/series/lnimsnus_series.shtml
Official URL:http://ebooks.worldscinet.com/ISBN/9789812567673/9789812567673_0015.html
Permanent URL: http://doi.org/10.5167/uzh-21671

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