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Research Article

Uniformly most accurate confidence intervals under weak restrictions

Received 13 May 2024, Accepted 26 Jul 2024, Published online: 01 Aug 2024
 

Abstract

The natural and commonly used measure of accuracy for a confidence interval (CI) is its length, but it only applies to bounded CI's. More seriously, it is not an invariant measure, creating chaos on selecting CI's. Using the probability of false coverage as a finite and invariant measure of accuracy for a CI, we establish the uniformly most accurate (UMA) CI under weak restriction, which substantially improves the classical UMA unbiased CI for simplicity and optimality.

2020 Mathematics Subject Classifications:

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The original Ghosh-Pratt identity, Eθ[length ofCX]=ΘPθ(θ~CX)dθ~, is corrected here.

Additional information

Funding

This research is partially supported by the National Natural Science Foundation of China (NSFC, Grant No. 11561073).

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