A Directional Approach for Testing Homogeneity

In recent years, likelihood-based higher order asymptotic methods have been developed to obtain inference for a scalar parameter of interest. In this paper, a directional test for a vector parameter of interest from a natural exponential family model is derived based on the likelihood-based higher order asymptotic methods. The proposed method is then applied to obtain p-value for testing homogeneity of inverse Gaussian scale-like parameters. Example and simulation results illustrate that the proposed method works almost perfectly.