Some simple corrected confidence intervals following a sequential test

In this paper, we consider the construction of confidence intervals for a secondary variable after a sequential test for a primary variable. Asymptotic moment expansions for randomly stopped averages are used to guide us to correct the naive confidence interval. Three corrected confidence intervals are investigated in terms of their coverage probability via Monte Carlo simulation. All three corrected confidence intervals are easy to calculate and improvements over the naive confidence interval for most of the situations considered. For the bivariate normal situation, one corrected confidence interval has its minimum coverage probability very close to its nominal confidence level and hence is recommended. (C) 2003 Elsevier B.V. All rights reserved.