On a decision rule using dichotomies for identifying the nonnegligible parameter in certain linear models

J. N. Srivastava and D. W. Mallenby

Journal of Multivariate Analysis, 1985, vol. 16, issue 3, 318-334

Abstract: 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" 2m 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.

Keywords: Search; linear; models; factorial; search; designs; probability; of; correct; search (search for similar items in EconPapers)
Date: 1985
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