Asymptotic considerations for selecting the best component of a multivariate normal population
type: Item
instance of: scholarly article
title: Asymptotic considerations for selecting the best component of a multivariate normal population
zbMATH Open document ID: 0611.62021
DOI: 10.1007/BF01897824
published in: Metrika
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/176014
review text: The problem discussed is that of selecting the component with the largest mean value in a k-variate normal population with unknown variance- covariance matrix with positive correlations. Let \(\mu_{[1]}\leq \mu_{[2]}\leq...\leq \mu_{[k]}\) be the ordered means of a k-variate normal population and let \(\Omega (\delta^*)=\{(\mu,\Sigma):\Sigma\) positive definite and \(\mu_{[k]}-\mu_{[k-1]}\geq \delta^*\}.\) The goal is to select the component with mean equal to \(\mu_{[k]}\) in such a way that the probability of correct selection is at least equal to \(P^*\) whenever (\(\mu,\Sigma)\in \Omega(\delta^*)\). Two-stage and sequential procedures having the \(P^*\) property are considered. The rates of convergence of the probability of correct selection of the procedures as \(\delta^*\to 0\) are presented. For a proposed sequential procedure, some results of the average sample number are presented.
Mathematics Subject Classification ID: 62F07
Mathematics Subject Classification ID: 62L05
zbMATH DE Number: 3988459
zbMATH Keywords: selecting the best component
zbMATH Keywords: indifference zone approach
zbMATH Keywords: two-stage selection procedures
zbMATH Keywords: multivariate normal
zbMATH Keywords: probability of correct selection
zbMATH Keywords: sequential procedures
zbMATH Keywords: rates of convergence
zbMATH Keywords: average sample number
author: Nitis Mukhopadhyay
reviewed by: Umesh D. Naik
MaRDI profile type: Publication
cites work: A Single-Sample Multiple Decision Procedure for Ranking Means of Normal Populations with known Variances
cites work: Q5610811
cites work: On the convergence rate of fixed-width sequential confidence intervals
cites work: Q4105098
cites work: A multivariate solution of the multivariate ranking and selection problem
cites work: Q3947006
cites work: Sequential point estimation of the mean when the distribution is unspecified
cites work: Q4747418
cites work: Q3915805
cites work: Multiple statistical decision theory: recent developments
cites work: On a Statistic which Arises in Selection and Ranking Problems
cites work: The exact approximation order in the central-limit-theorem for random summation
cites work: Some comments on two-stage selection procedures
cites work: A consistent and asymptotically efficient two-stage procedure to construct fixed width confidence intervals for the mean
cites work: Convergence rates of sequential confidence intervals and tests for the mean of a u-statistic
cites work: Q3709694
cites work: Q3675323
cites work: Q3725328
cites work: On two-stage selection procedures and related probability-inequalities
cites work: A Sequential Procedure for Selecting the Largest of $k$ Means
cites work: Second order approximations for sequential point and interval estimation
OpenAlex ID: W2055706324
description: scientific article; zbMATH DE number 3988459