A sharp necessary condition for admissibility of sequential tests - necessary and sufficient conditions for admissibility of SPRT's
type: Item
instance of: scholarly article
title: A sharp necessary condition for admissibility of sequential tests - necessary and sufficient conditions for admissibility of SPRT's
zbMATH Open document ID: 0539.62093
author: Arthur Cohen
author: Ester Samuel-Cahn
author: Lawrence Brown
published in: The Annals of Statistics
publication date: 1983-01-01T00:00:00Z
review text: Let \(X_ 1,X_ 2,..\). be i.i.d. \(N(\theta\),1) random variables, and consider the problem of sequentially testing \(H_ 0:\theta \leq 0\) versus \(H_ 1:\theta>0\). If N is a stopping rule of a sequential test, the underlying risk is \(cE_{\theta}N+P_{\theta}(error)\). Let \(S_ n=X_ 1+...+X_ n\), \(n\geq 1\), and let \(\{a_ n,b_ n\), \(n\geq 1\}\) be suitable sequences of constants. It is known that all admissible tests must be monotone in that N must be of the form \(N=\inf \{n\geq 1: S_ n\leq a_ n\) or \(S_ n\geq b_ n\}\), where \(H_ 0\) is accepted if \(S_ N\leq a_ N\), and rejected if \(S_ N\geq b_ N.\) The authors show that any admissible test must in addition satisfy \(b_ n-a_ n\leq 2\bar b(c).\) The bound is sharp in that the symmetric test with \(a_ n=-\bar b(c)\) and \(b_ n=\bar b(c)\) is admissible. As a consequence of the above result the authors obtain necessary and sufficient conditions for admissibility of an SPRT (sequential probability ratio test).
Mathematics Subject Classification ID: 62L10
Mathematics Subject Classification ID: 62C15
Mathematics Subject Classification ID: 62L99
zbMATH DE Number: 3858238
zbMATH Keywords: Wiener process
zbMATH Keywords: stopping rule
zbMATH Keywords: risk
zbMATH Keywords: monotone
zbMATH Keywords: necessary and sufficient conditions for admissibility
zbMATH Keywords: sequential probability ratio test
reviewed by: Rasul A. Khan
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176346169
OpenAlex ID: W2072322227
DOI: 10.1214/AOS/1176346169
description: scientific article; zbMATH DE number 3858238