Partial Conditioning for Inference of Many-Normal-Means with H\"older Constraints

TL;DR

This paper introduces a novel partial conditioning method for valid and efficient inference of many-normal-means with H"older constraints, improving upon existing fiducial and conservative approaches.

Contribution

The paper proposes a new partial conditioning technique for inferential models, specifically addressing the many-normal-means problem with H"older constraints, enhancing validity and efficiency.

Findings

Partial conditioning outperforms fiducial methods in validity.

It surpasses conservative methods in efficiency.

The approach is applicable to H"older-constrained many-normal-means problems.

Abstract

Inferential models have been proposed for valid and efficient prior-free probabilistic inference. As it gradually gained popularity, this theory is subject to further developments for practically challenging problems. This paper considers the many-normal-means problem with the means constrained to be in the neighborhood of each other, formally represented by a H\"older space. A new method, called partial conditioning, is proposed to generate valid and efficient marginal inference about the individual means. It is shown that the method outperforms both a fiducial-counterpart in terms of validity and a conservative-counterpart in terms of efficiency. We conclude the paper by remarking that a general theory of partial conditioning for inferential models deserves future development.