Asymptotic Expansion for Sampling Distribution and Sample Size in Statistical Inference Ⅲ—The Modified Likelihood Ratio Λ-Test in the Noncentral Case

摘要

This is the third article on the subject stated in the title, treating the asymptotic expansion formula for the OC function of the modified Λ-test. According to the idea and approaching procedure in our first article (Siotani et al, 1995), the reference domain of parameters for making the expansion formula valid was set up. Then an approximate upper bound on the absolute error of the treated expanded OC function was constructed numerically and experimentally over the reference domain in such a way that it provides the guarantee for the practical validity of the expanded OC function and method of determining an effective sample size for designing the test procedure satisfying some requirements on the power of the test.