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

Author

Listed:
  • Srivastava, J. N.
  • Mallenby, D. W.

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.

Suggested Citation

  • Srivastava, J. N. & Mallenby, D. W., 1985. "On a decision rule using dichotomies for identifying the nonnegligible parameter in certain linear models," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 318-334, June.
    • Handle: RePEc:eee:jmvana:v:16:y:1985:i:3:p:318-334
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