Calibrating Confidence Coefficients

Abstract

Abstract Two approaches for dealing with the problem of poor coverage probabilities of certain standard confidence intervals are proposed. The first is a recommendation that the actual coverage be estimated directly from the data and its value reported in addition to the nominal level. This is achieved through a combination of computer simulation and density estimation. The asymptotic validity of the procedure is proved for a number of common situations. A classical example is the nonparametric estimation of the variance of a population using the normal-theory interval. Here it is shown that the estimated coverage probability consistently estimates the true coverage probability if the population distribution possesses a finite sixth moment. The second approach is more traditional. It is a procedure for modifying an interval to yield improved coverage properties. Given a confidence interval, its estimated coverage probability obtained in the first approach is used to alter the nominal level of the interval...