Distribution-free Detection of a Submatrix
Statistics Theory
2016-04-27 v1 Methodology
Statistics Theory
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 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.
Cite
@article{arxiv.1604.07449,
title = {Distribution-free Detection of a Submatrix},
author = {Ery Arias-Castro and Yuchao Liu},
journal= {arXiv preprint arXiv:1604.07449},
year = {2016}
}