Positive regression dependence on subsets for multivariate χ² random variables

Oregon Convention Center 

We show a dependence condition, positive regression dependence on subsets, for multivariate X² random variables of a generalized Wishart type. This class of random variables occurs asymptotically on collections of test statistics arising from analysis of variance models. The dependence condition holds when the test statistics are generated under an arbitrary combination of null and alternative hypotheses, where the subset on which positive regression dependence holds is those test statistics realized under the null hypothesis. The condition is therefore sufficient for application of several multiple testing adjustment procedures including false discovery rate adjustment, and useful for high-dimensional settings when differences between multiple strata is of inferential interest.

multiple testing

positive regression dependence

false discovery rate

positive regression dependence on subsets 

IMS