On randomized confidence intervals for the binomial probability

TL;DR

This paper explores randomized and data-randomized confidence intervals for the binomial probability, extending existing methods and discussing their practical applications.

Contribution

It introduces extensions of Stevens' randomized interval and highlights the advantages of Korn's data-randomized interval for binomial confidence estimation.

Findings

Extensions of Stevens' randomized confidence intervals are proposed.

Additional attractive features of Korn's data-randomized interval are identified.

The paper discusses practical considerations for using these intervals.

Abstract

Suppose that X_1,X_2,...,X_n are independent and identically Bernoulli(theta) distributed. Also suppose that our aim is to find an exact confidence interval for theta that is the intersection of a 1-\alpha/2 upper confidence interval and a 1-\alpha/2 lower confidence interval. The Clopper-Pearson interval is the standard such confidence interval for theta, which is widely used in practice. We consider the randomized confidence interval of Stevens, 1950 and present some extensions, including pseudorandomized confidence intervals. We also consider the "data-randomized" confidence interval of Korn, 1987 and point out some additional attractive features of this interval. We also contribute to the discussion about the practical use of such confidence intervals.