Neyman's C(α) test for the shape parameter of the exponential power class

Abstract

Tests based on Neyman's C(α) approach are proposed for the shape parameter of the exponential power distribution (EPD). Earlier work on the maximum likelihood estimators for the EPD shows that asymptotic normality is hard to establish under the classic regularity conditions due to a discontinuity in its density functions and non-dominated third derivatives. Nevertheless, local asymptotic optimality of the test can be established via Le Cam's differentiability in quadratic mean, with local alternatives of order . We mainly focus on setting the null of the shape parameter to 1 and 2, corresponding, respectively, to the Laplace and normal distributions. Further, we extend the results to the bivariate EPD. A Monte Carlo study illustrates the theoretical results. Real data applications are also given.