Dominance of likelihood ratio tests under cone constraints
type: Item
instance of: scholarly article
title: Dominance of likelihood ratio tests under cone constraints
zbMATH Open document ID: 0774.62057
published in: The Annals of Statistics
publication date: 1993-05-16T00:00:00Z
review text: Let \(Y\) be a \(k\)-dimensional random vector having a normal distribution \(N_ k(\theta,\Gamma)\) with \(\theta\) restricted to belong to a closed convex cone \(C\) of \(\mathbb R^ k\). Let \(L\) be a linear subspace and consider the problem of testing \(H_ 0: \theta\in C\cap L\) against \(H_ a-H_ 0\) where \(H_ a: \theta\in C\). Under suitable conditions the authors prove the dominance of the LRT (likelihood ratio test), and also provide conditions which guarantee the equivalence of the LRT and a simple test. The cases of known and unknown variances are considered and examples are discussed to illustrate the results.
reviewed by: Rasul A. Khan
Mathematics Subject Classification ID: 62H15
Mathematics Subject Classification ID: 62F03
Mathematics Subject Classification ID: 62F30
zbMATH DE Number: 166854
zbMATH Keywords: testing restricted hypotheses
zbMATH Keywords: obliqueness
zbMATH Keywords: normal distribution
zbMATH Keywords: closed convex cone
zbMATH Keywords: linear subspace
zbMATH Keywords: dominance
zbMATH Keywords: equivalence
zbMATH Keywords: known and unknown variances
author: José A. Menéndez
author: Cristina Rueda
author: Bonifacio Salvador
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176348904
OpenAlex ID: W2011081090
DOI: 10.1214/AOS/1176348904
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description: scientific article; zbMATH DE number 166854