  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.
