Repeated significance tests for exponential families
type: Item
instance of: scholarly article
title: Repeated significance tests for exponential families
zbMATH Open document ID: 0665.62081
author: Inchi Hu
published in: The Annals of Statistics
publication date: 1988-01-01T00:00:00Z
review text: To test \(H_ 0:\theta \in \Theta_ 0\subset \Theta\), the sequence of log-likelihood ratio statistics \(\lambda (n)=\sup_{\theta \in \Theta}l_ n(\theta)-\sup_{\theta \in \Theta_ 0}l_ n(\theta)\) is considered. Let m, \(m_ 0\), a and \(c<a\) be given numbers and let \(T=\inf \{n:\) \(n\geq m_ 0\), \(\lambda (n)>a\}\). The repeated significance test (RST) rejects \(H_ 0\) if \(T\leq m\). The modified RST (MRST) rejects \(H_ 0\) if either \(T\leq m\) or \(T>m\) and \(\lambda (n)>c.\) The power and significance level of RST and MRST are discussed in detail. Numerical and Monte Carlo results are presented.
Mathematics Subject Classification ID: 62L10
Mathematics Subject Classification ID: 62F03
zbMATH DE Number: 4088771
zbMATH Keywords: sequence of log-likelihood ratio statistics
zbMATH Keywords: repeated significance test
zbMATH Keywords: power
zbMATH Keywords: significance level
zbMATH Keywords: Monte Carlo results
reviewed by: Ryszard Zieliński
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176351059
OpenAlex ID: W1984658205
DOI: 10.1214/AOS/1176351059
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description: scientific article; zbMATH DE number 4088771