10/17/2014

Post date: Oct 21, 2014 3:21:11 AM

"Optimal Tests of Independence with Applications to Testing More Structures " (job talk practice)

Fang Han, Department of Biostatistics, Johns Hopkins University

Abstract: We consider the problem of testing mutual independence of all entries in a d-dimensional random vector based on n independent observations with d possibly larger than n. For this, we consider two families of distribution-free test statistics that converge weakly to an extreme value type I distribution. We further study the powers of the corresponding tests against the sparse alternative and justify certain optimality. As important examples, we show that the tests based on Kendall's tau and Spearman's rho are rate optimal tests of independence. For further generalization, we consider accelerating the rate of convergence via approximating the exact distributions of the test statistics. We also study the tests of two more structural hypotheses: m-dependence and data homogeneity. For these, we propose two rank-based tests and show their optimality.