Analysis of sequential stopping rules

Sequential stopping rules applied to confidence interval procedures (CIPs) may lead to coverage that is less than nominal. This paper introduces a method for estimating coverage functions analytically in order to evaluate the potential loss of coverage. This method also provides an estimate for the distribution of the stopping time of the procedure. Knowledge of coverage functions could help evaluate and compare confidence interval procedures while avoiding lengthy empirical testing. Numerical implementation of our method shows that analytical coverage functions approximate those calculated empirically. Analytical coverage functions can be used to explain why many sequential procedures do not provide adequate coverage.