Partial conditioning for inference of many-normal-means with Hölder constraints

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 b...

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Bibliographic Details
Published inInternational journal of approximate reasoning Vol. 159; p. 108946
Main Authors Yang, Jiasen, Wang, Xiao, Liu, Chuanhai
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.08.2023
Subjects
Dempster-Shafer theory
Fiducial argument
Hölder space
Lipschitz space
Nonparametric regression
Lipschitz space
Dempster-Shafer theory
Fiducial argument
Hölder space
Nonparametric regression
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ISSN0888-613X
1873-4731
DOI10.1016/j.ijar.2023.108946

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Summary: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 Hölder 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.
ISSN:0888-613X
1873-4731
DOI:10.1016/j.ijar.2023.108946