Reliability of parametrically specified model of measurements
type: Item
instance of: scholarly article
title: Reliability of parametrically specified model of measurements
zbMATH Open document ID: 0706.62020
author: I. V. Mitin
author: A. I. Chulichkov
published in: Moscow University Physics Bulletin
publication date: 1989-01-01T00:00:00Z
review text: In \textit{Yu. P. Pyt'ev}, Sov. Math., Dokl. 36, No.1, 96-100 (1987); translation from Dokl. Akad. Nauk SSSR 295, 542-545 (1987; Zbl 0645.62109), the reliability of a simple hypothesis vs a simple alternative was defined as \(\alpha (x)=\inf \{\alpha:\phi^{\alpha}(x)=1\}\), where x is a given observation and \(\phi^{\alpha}\) is the UMP test at the significance level \(\alpha\). A more general definition of reliability of a composite hypothesis vs composite alternative was also introduced. In this paper, an approximation of \(\alpha\) (x) for smooth densities is discussed. As examples the reliability of Gaussian models are computed. Comment: compare the reliability \(\alpha\) (x) with the critical level in \textit{E. L. Lehmann}, Testing statistical hypotheses (1959; Zbl 0089.141), p. 150, \([\alpha (x)=\inf \{\alpha:\) \(x\in S_{\alpha}\}\), where \(S_{\alpha}\) is the rejection region] or with p-values in the second edition of this book (1986; Zbl 0608.62020), p. 170.
reviewed by: Ryszard Zieliński
Mathematics Subject Classification ID: 62F03
Mathematics Subject Classification ID: 62A01
Mathematics Subject Classification ID: 62G10
zbMATH DE Number: 4159861
zbMATH Keywords: reliability of statistical models
zbMATH Keywords: smooth densities
zbMATH Keywords: reliability of Gaussian models
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4159861