On a decision rule using dichotomies for identifying the nonnegligible parameter in certain linear models
type: Item
instance of: scholarly article
title: On a decision rule using dichotomies for identifying the nonnegligible parameter in certain linear models
zbMATH Open document ID: 0602.62048
DOI: 10.1016/0047-259X(85)90024-7
author: D. W. Mallenby
author: Jagdish N. Srivastava
published in: Journal of Multivariate Analysis
publication date: 1985-01-01T00:00:00Z
review text: Consider the class of linear models (with uncorrelated observation, each having variance \(\sigma^ 2)\), in which it is known that at most k (location) parameters are negligible, but it is not known which are negligible. The problem is to identify the nonnegligible parameters. In this paper, for \(k=1\), and under certain restrictions on the model, a technique is developed for solving this problem, which has the feature of requiring (in an information theoretic sense) the minimum amount of computation. (It can ''search through'' \(2^ m\) objects, using m ''steps''.) The technique consists of dichotomizing the set of parameters (one known subset possibly containing the nonnegligible element, and the other not), using chi-square variables. A method for computing the probability that the correct parameter is identified, is presented, and an important application to factorial search designs is established.
Mathematics Subject Classification ID: 62H15
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 62K15
Mathematics Subject Classification ID: 05A17
zbMATH DE Number: 3971999
zbMATH Keywords: probability of correct search
zbMATH Keywords: dichotomization of parameter set
zbMATH Keywords: linear models
zbMATH Keywords: location
zbMATH Keywords: nonnegligible parameters
zbMATH Keywords: factorial search designs
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3971999