Conditional coverage probability of confidence intervals in errors-in-variables and related models

Abstract

Gleser and Hwang (1987) show that there exists no nontrivial confidence interval with finite expected length for many errors-in-variables and related models. Nonetheless, the validity of using these confidence intervals only when their realizations are of finite length remains uninvestigated. We scrutinize this practice from a conditional frequentist viewpoint and find it not justifiable. It is shown that under some conditions, the minimum coverage probability of the confidence interval is zero if conditioning on the event that the confidence interval has finite length. The result is then applied to confirm Neyman's conjecture for Fieller's confidence sets.