On optimal decision rules for signs of parameters
type: Item
instance of: scholarly article
title: On optimal decision rules for signs of parameters
zbMATH Open document ID: 0619.62065
author: Yosef Hochberg
author: Marc E. Posner
published in: The Annals of Statistics
publication date: 1986-01-01T00:00:00Z
review text: Let X have a bivariate normal distribution with known covariance matrix and expectation \(\theta\). Interest is on an optimal decision rule for the signs of the components of \(\theta\) which is based on X. Optimality means to maximize the expected number of correct decisions - when \(\theta\) tends to zero - under all decision rules which are symmetric, upper convex and satisfying \(P_{\theta}(no\) incorrect decision) \(\geq 1- \alpha\) for all \(\theta\). The problem can be formulated as a linear programming problem. Its solutions are discussed using the Neyman-Pearson lemma. The results extend earlier results by \textit{R. Bohrer} and \textit{M. J. Schervish}, Proc. Natl. Acad. Sci. USA 77, 52-56 (1980; Zbl 0428.62008).
reviewed by: O. Krafft
Mathematics Subject Classification ID: 62J15
Mathematics Subject Classification ID: 62C99
zbMATH DE Number: 4005377
zbMATH Keywords: double cross
zbMATH Keywords: locally optimal
zbMATH Keywords: generalized optimization functions
zbMATH Keywords: decision on signs of parameters
zbMATH Keywords: bivariate normal distribution
zbMATH Keywords: optimal decision rule
zbMATH Keywords: expected number of correct decisions
zbMATH Keywords: linear programming
zbMATH Keywords: Neyman-Pearson lemma
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176349950
OpenAlex ID: W1968012258
DOI: 10.1214/AOS/1176349950
description: scientific article; zbMATH DE number 4005377