A Unified Approach for Constructing Confidence Intervals and Hypothesis Tests Using h-function

TL;DR

The paper presents the h-function method, a unified approach to construct exact confidence intervals and hypothesis tests, improving existing intervals by ensuring exactness and subset relations.

Contribution

It introduces a general, unifying framework that transforms approximate intervals into exact ones and refines existing intervals to be subsets, enhancing statistical inference accuracy.

Findings

Successfully applied to real datasets demonstrating improved intervals.

Provides a unified framework for constructing exact tests and confidence intervals.

Enhances the precision and reliability of statistical inference.

Abstract

We introduce a general method, named the h-function method, to unify the constructions of level-alpha exact test and 1-alpha exact confidence interval. Using this method, any confidence interval is improved as follows: i) an approximate interval, including a point estimator, is modified to an exact interval; ii) an exact interval is refined to be an interval that is a subset of the previous one. Two real datasets are used to illustrate the method.