Combining independent one-sided noncentral t or normal mean tests
type: Item
instance of: scholarly article
title: Combining independent one-sided noncentral t or normal mean tests
zbMATH Open document ID: 0588.62011
author: John I. Marden
published in: The Annals of Statistics
publication date: 1985-01-01T00:00:00Z
review text: Let \(T_ 1,T_ 2,...,T_ n\) be independent where the distribution of \(T_ i\) depends on \(\theta_ i,\quad i=1,2,...,n\). The problem is to test the hypothesis \(H_ 0:\theta_ i=0,\quad i=1,...,n\), versus \(H_ A:\theta =(\theta_ 1,...,\theta_ n)\in \Theta_ A=R^ n_+\setminus \{0\}\), all the procedures in question being based on the observed significance levels \(p_ i\) of the individuals \(T_ i,\quad p_ i=P_ 0(T_ i\geq t_ i)\) where \(P_ 0\) represents the null distribution of \(T=(T_ 1,...,T_ n).\) Two cases are investigated. 1) \(T_ i\) has normal distribution; 2) \(T_ i\) has noncentral t-distribution with \(\nu_ i\) degrees of freedom and noncentrality parameter \(\theta_ i,\quad i=1,2,...,n.\) Minimal complete classes of the procedures are found. It is shown particularly that the likelihood ratio tests and Tippett's procedure are admissible in both cases, and Fisher's and the inverse normal procedures are admissible in the normal case but inadmissible in the t-case.
Mathematics Subject Classification ID: 62C15
Mathematics Subject Classification ID: 62F03
Mathematics Subject Classification ID: 62C07
Mathematics Subject Classification ID: 62H15
Mathematics Subject Classification ID: 62C10
zbMATH DE Number: 3945037
zbMATH Keywords: one-sided tests of significance
zbMATH Keywords: inverse logistic
zbMATH Keywords: sum of significance levels procedures
zbMATH Keywords: generalized Bayes tests
zbMATH Keywords: combination procedures
zbMATH Keywords: Fisher's procedure
zbMATH Keywords: observed significance levels
zbMATH Keywords: normal distribution
zbMATH Keywords: noncentral t-distribution
zbMATH Keywords: Minimal complete classes
zbMATH Keywords: likelihood ratio tests
zbMATH Keywords: Tippett's procedure
zbMATH Keywords: inverse normal procedures
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176349754
OpenAlex ID: W2059310989
DOI: 10.1214/AOS/1176349754
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description: scientific article; zbMATH DE number 3945037