Interval estimation via tail functions

Abstract

In this paper we describe a new methodology for constructing confidence intervals. The idea is to specify the tail cutoff areas in terms of a function of the target parameter rather than as constants. This function, called the tail function, can be engineered so as to provide shorter confidence intervals when prior information is available. It can also be used to improve the coverage properties of approximate confidence intervals. We illustrate the methodology by applying it to inference on the normal mean and binomial proportion, and develop measures of the resulting improvements. Guidelines for choosing the optimal tail function in any situation are provided, and the relationship with Bayesian inference is discussed.