Testing Hypotheses for Ratios of Normal Density

This paper discusses the test problem concerning ratios of two normal density functions. We present large sample tests based on asymptotic normality of some statistics and the test based on generalized p-values, respectively. Some frequency properties of the generalized p-values are proved. We conclude from simulation results that the performance of the test based on generalized p-values is better than the large sample tests in small sample cases.