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February 2013 On the maximal size of large-average and ANOVA-fit submatrices in a Gaussian random matrix
Xing Sun, Andrew B. Nobel
Bernoulli 19(1): 275-294 (February 2013). DOI: 10.3150/11-BEJ394

Abstract

We investigate the maximal size of distinguished submatrices of a Gaussian random matrix. Of interest are submatrices whose entries have an average greater than or equal to a positive constant, and submatrices whose entries are well fit by a two-way ANOVA model. We identify size thresholds and associated (asymptotic) probability bounds for both large-average and ANOVA-fit submatrices. Probability bounds are obtained when the matrix and submatrices of interest are square and, in rectangular cases, when the matrix and submatrices of interest have fixed aspect ratios. Our principal result is an almost sure interval concentration result for the size of large average submatrices in the square case.

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Xing Sun. Andrew B. Nobel. "On the maximal size of large-average and ANOVA-fit submatrices in a Gaussian random matrix." Bernoulli 19 (1) 275 - 294, February 2013. https://doi.org/10.3150/11-BEJ394

Information

Published: February 2013
First available in Project Euclid: 18 January 2013

zbMATH: 1259.62062
MathSciNet: MR3019495
Digital Object Identifier: 10.3150/11-BEJ394

Rights: Copyright © 2013 Bernoulli Society for Mathematical Statistics and Probability

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Vol.19 • No. 1 • February 2013
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