Distribution-free detection of a submatrix

Ery Arias-Castro and Yuchao Liu

Journal of Multivariate Analysis, 2017, vol. 156, issue C, 29-38

Abstract: We consider the problem of detecting the presence of a submatrix with larger-than-usual values in a large data matrix. This problem was considered in Butucea and Ingster (2013) under a one-parameter exponential family, and one of the procedures they analyzed is the scan test. Taking a nonparametric stance, we show that a calibration by permutation leads to the same (first-order) asymptotic performance. This is true for the two types of permutations we consider. We also study the corresponding rank-based variants and quantify precisely the loss in asymptotic power.

Keywords: Submatrix detection; Permutation test; Rank method; Exponential family; Asymptotic power; Gene expression data (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.jmva.2017.01.013

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