Inadmissibility of the Best Invariant Test When the Moment is Infinite Under One of the Hypotheses

Autor:	S. K. Perng, Martin Fox
Rok vydání:	1969
Předmět:	Moment (mathematics) Combinatorics Distribution function Statistical analysis Invariant (physics) Random variable Statistical hypothesis testing Mathematics
Zdroj:	Ann. Math. Statist. 40, no. 4 (1969), 1483-1485
ISSN:	0003-4851
DOI:	10.1214/aoms/1177697520
Popis:	Let X and Y be real valued random variables with joint density g sub i (y) f sub i (x-theta, y) under the hypothesis H sub i (i = 1, 2). Assume theta is unknown. The best invariant test of H sub 1 vs H sub 2 is known to be admissible if X has a finite first moment under both hypotheses. The present paper provides an example in which admissibility fails if under one hypothesis the first moment is infinite. (Author)
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a13600b9f6a5a597595967d8deb0efa2 https://doi.org/10.1214/aoms/1177697520 Zobrazit plný text záznamu