Nonnull asymptotic distributions of three classic criteria in nonlinear Birnbaum-Saunders regressions

Abstract

In this paper, we derive nonnull asymptotic expansions for the cumulative distribution functions of the likelihood ratio, Wald, and Rao score test statistics in nonlinear Birnbaum-Saunders regression models under a sequence of Pitman alternatives. The second-order local power of these three likelihood-based tests, which are equivalent to first-order, is compared analytically. We then provide an explicit and easily applicable expression for the difference in power of any two criteria, and, hence, the user can choose the most powerful test to make inferences on the regression parameters in the class of nonlinear Birnbaum-Saunders regression models. We also provide a real data example for illustrative purposes.