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arxiv: 1604.07449 · v1 · pith:L2KWCWFXnew · submitted 2016-04-25 · 🧮 math.ST · stat.ME· stat.TH

Distribution-free Detection of a Submatrix

Ery Arias-Castro , Yuchao Liu This is my paper
classification 🧮 math.ST stat.MEstat.TH
keywords asymptoticconsiderproblemsubmatrixtestanalyzedbutuceacalibration
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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 test 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 precisely quantify the loss in asymptotic power.

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