A new method in introducing the uniformly most accurate confidence set

Abstract

The uniformly most accurate (UMA) is an important optimal approach in interval estimation, but the current literature often introduces it in a confusing way, rendering the learning, teaching and researching of UMA problematic. Two major aspects cause this confusion. First, UMA is often interpreted to maximize the accuracy of coverage, but in fact, it minimizes the falseness of coverage. Second, even though it is a major concept in interval estimation, the most common proof of UMA requires the result of the uniformly most powerful (UMP) test, which has nothing to do with the rest of the interval estimation concept. To resolve these issues, in this article we propose a new method of introducing UMA that aligns its terminology with its definition and proves it entirely within the concept of confidence interval, independent to the knowledge of hypothesis testing. The new method eliminates the aforementioned confusion and allows for a smoother learning, teaching and research experience in UMA.

KEYWORDS:

• Confidence set
• confidence interval
• interval estimation
• optimal set

Disclosure statement

No potential conflict of interest was reported by the authors.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.