The Power of Confidence Intervals

TL;DR

This paper explores the reliability and power of confidence intervals in frequentist methods, highlighting the optimal bias of the maximum likelihood estimator for bounded parameters.

Contribution

It establishes a connection between confidence interval power and reliability, and identifies the maximum likelihood estimator as optimally biased near boundaries.

Findings

Biased methods with large power near boundaries are desirable.

Maximum likelihood estimator has optimal bias for bounded parameters.

Confidence interval power relates to their reliability.

Abstract

We connect the power of Confidence Intervals in different Frequentist methods to their reliability. We show that in the case of a bounded parameter a biased method which near the boundary has large power in testing the parameter against larger alternatives and small power in testing the parameter against smaller alternatives is desirable. Considering the recently proposed methods with correct coverage, we show that the Maximum Likelihood Estimator method has optimal bias.