On a decision rule using dichotomies for identifying the nonnegligible parameter in certain linear models
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.
scientific article; zbMATH DE number 3971999
scientific article