Admissible, consistent multiple testing with applications

Abstract

For multivariate normal models and exponential family models a multiple testing stepwise method is offered that is both admissible and consistent. The method is readily adaptable to selecting variables in linear regression models where it is akin to the forward selection method plus a screening stage plus a sign compatibility stage. The method is also adaptable to testing the local odds ratios in contingency tables in which the categories are ordered. Examples and simulations are included.