Test inversion bootstrap confidence intervals

In this paper we explore the theoretical and practical implications of using bootstrap test inversion to construct confidence intervals. In the presence of nuisance parameters, we show that the coverage error of such intervals is O(n(-1/2)) which may be reduced to O(n(-1)) if a Studentized statistic is used. We present three simulation studies and compare the performance of test inversion methods with established methods on the problem of estimating a confidence interval for the dose-response parameter in models of the Japanese atomic bomb survivors data.