Bernoulli

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  • Volume 19, Number 1 (2013), 275-294.

On the maximal size of large-average and ANOVA-fit submatrices in a Gaussian random matrix

Xing Sun and Andrew B. Nobel

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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.

Article information

Source
Bernoulli Volume 19, Number 1 (2013), 275-294.

Dates
First available in Project Euclid: 18 January 2013

Permanent link to this document
http://projecteuclid.org/euclid.bj/1358531750

Digital Object Identifier
doi:10.3150/11-BEJ394

Mathematical Reviews number (MathSciNet)
MR3019495

Zentralblatt MATH identifier
1259.62062

Keywords
analysis of variance data mining Gaussian random matrix large average submatrix random matrix theory second moment method

Citation

Sun, Xing; Nobel, Andrew B. On the maximal size of large-average and ANOVA-fit submatrices in a Gaussian random matrix. Bernoulli 19 (2013), no. 1, 275--294. doi:10.3150/11-BEJ394. http://projecteuclid.org/euclid.bj/1358531750.


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