Local power of some likelihood‐based tests in multivariate Student‐t regression models

Abstract

The Student‐ distribution has proved to be a useful alternative to the traditional normal distribution, mainly to deal with heavy tails and when robust estimation is desired. We consider the multivariate Student‐ regression model and derive the nonnull asymptotic expansions (under a sequence of Pitman alternatives) of the distribution functions of the likelihood ratio, Wald, Rao score, and gradient test statistics for testing a subset of regression parameters in this class of multivariate regression models. On the basis of the nonnull asymptotic expansions derived, the power of all four tests, which are equivalent to the first order, are compared. We provide conditions in which one test can be more locally powerful than the other one in this class of multivariate regression models and, hence, one can choose the most powerful test based on the general conditions.