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A Quasi-Bayesian Approach to Estimating Parameters for Mixtures of Normal Distributions


  • Hamilton, James D


This article proposes a very tractable approach to estimating parameters for mixtures of normal distributions. The analyst proceeds as if, in addition to the data, he or she had observed some pseudo data points drawn from each distribution whose values reflect his or her priors. The approach eliminates the singularities associated with maximum likelihood estimation and offer guidance for choosing among alternative local maximum likelihood estimates. Monte Carlo analysis established its consistent potential to improve mean squared errors. Data sets on which maximum likelihood estimation has presented difficulties are shown to be readily analyzed with the quasi-Bayesian procedure.

Suggested Citation

  • Hamilton, James D, 1991. "A Quasi-Bayesian Approach to Estimating Parameters for Mixtures of Normal Distributions," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(1), pages 27-39, January.
  • Handle: RePEc:bes:jnlbes:v:9:y:1991:i:1:p:27-39

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    References listed on IDEAS

    1. Conlisk, John, 1989. "Three Variants on the Allais Example," American Economic Review, American Economic Association, vol. 79(3), pages 392-407, June.
    2. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    3. Machina, Mark J, 1987. "Choice under Uncertainty: Problems Solved and Unsolved," Journal of Economic Perspectives, American Economic Association, vol. 1(1), pages 121-154, Summer.
    4. Camerer, Colin F, 1989. "An Experimental Test of Several Generalized Utility Theories," Journal of Risk and Uncertainty, Springer, vol. 2(1), pages 61-104, April.
    5. Fishburn, Peter C., 1983. "Transitive measurable utility," Journal of Economic Theory, Elsevier, vol. 31(2), pages 293-317, December.
    6. Battalio, Raymond C & Kagel, John H & Jiranyakul, Komain, 1990. "Testing between Alternative Models of Choice under Uncertainty: Some Initial Results," Journal of Risk and Uncertainty, Springer, vol. 3(1), pages 25-50, March.
    7. Tversky, Amos & Kahneman, Daniel, 1986. "Rational Choice and the Framing of Decisions," The Journal of Business, University of Chicago Press, vol. 59(4), pages 251-278, October.
    8. Dekel, Eddie, 1986. "An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom," Journal of Economic Theory, Elsevier, vol. 40(2), pages 304-318, December.
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