Confidence intervals for intentionally biased estimators

TL;DR

This paper introduces three new confidence intervals centered at intentionally biased estimators, balancing coverage probability and interval length, with broad practical applicability.

Contribution

It develops novel confidence interval methods centered at biased estimators, improving coverage and length trade-offs compared to traditional unbiased approaches.

Findings

First CI has higher coverage for levels above 91.7%.

Second CI reduces length at some coverage cost.

Third CI further shortens intervals using a convex combination.

Abstract

We propose and study three confidence intervals (CIs) centered at an estimator that is intentionally biased to reduce mean squared error. The first CI simply uses an unbiased estimator's standard error; compared to centering at the unbiased estimator, this CI has higher coverage probability for confidence levels above 91.7%, even if the biased and unbiased estimators have equal mean squared error. The second CI trades some of this "excess" coverage for shorter length. The third CI is centered at a convex combination of the two estimators to further reduce length. Practically, these CIs apply broadly and are simple to compute.