ASYMPTOTIC EXPANSIONS FOR E_θ(t) AND E_θ(^-x_t) WHICH APPEAR IN THE REPEATED SIGNIFICANCE TESTS FOR THE NORMAL MEANS

Abstract

This paper continues the project of Takahashi (1987) to obtain asymptotic expansions forE_θ(t) and E_θ(^-x_t) up to the terms involving a^-1 and a^-2, respectively, as a→∞, where t is the one-sided stopping time for testing the hypothesis that the normal mean is zero.
AMS 1980 subject classifications. Primary 60F05, 62L12; secondary 60K05.