Shortest fixed-width confidence intervals for a bounded parameter: The Push algorithm

TL;DR

This paper introduces the Push algorithm, an optimal method for computing shortest fixed-width confidence intervals for bounded parameters, applicable to various distributions and demonstrated on real WHO data.

Contribution

The paper extends the Push algorithm to a broader class of distributions, providing a method for shortest fixed-width confidence intervals with proven optimality.

Findings

Outperforms standard confidence interval methods in multiple distributions

Provides shortest fixed-width confidence intervals for bounded parameters

Improves upon the traditional z-interval in normal distribution cases

Abstract

We present a method for computing optimal fixed-width confidence intervals for a single, bounded parameter, extending a method for the binomial due to Asparaouhov and Lorden, who called it the Push algorithm. The method produces the shortest possible non-decreasing confidence interval for a given confidence level, and if the Push interval does not exist for a given width and level, then no such interval exists. The method applies to any bounded parameter that is discrete, or is continuous and has the monotone likelihood ratio property. We demonstrate the method on the binomial, hypergeometric, and normal distributions with our available R package. In each of these distributions the proposed method outperforms the standard ones, and in the latter case even improves upon the $z$-interval. We apply the proposed method to World Health Organization (WHO) data on tobacco use.