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Estimation of Multinomial Probabilities under a Model Constraint


  • Gupta, A. K.
  • Ehsanes Saleh, A. K. Md.


In this paper estimation of the probabilities of a multinomial distribution has been studied. The five estimators considered are: unrestricted estimator (UE), restricted estimator (RE) (under model ), preliminary test estimator (PTE) based on a test of the model , shrinkage estimator (SE) and the positive-rule shrinkage estimator (PRSE). Asymptotic distributions of these estimators are given under Pitman alternatives and the asymptotic risk under a quadratic loss has been evaluated. The relative performance of the five estimators is then studied with respect to their asymptotic distributional risks (ADR). It is seen that neither of the preliminary test and shrinkage estimators dominates the other, though each fares well relative to the other estimators. However, the positive rule estimator is recommended for use for dimension 3 or more while the PTE is recommended for dimension less than 3.

Suggested Citation

  • Gupta, A. K. & Ehsanes Saleh, A. K. Md., 1996. "Estimation of Multinomial Probabilities under a Model Constraint," Journal of Multivariate Analysis, Elsevier, vol. 58(2), pages 151-161, August.
  • Handle: RePEc:eee:jmvana:v:58:y:1996:i:2:p:151-161

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    Cited by:

    1. Gupta, A.K. & Nguyen, T. & Pardo, L., 2006. "Preliminary Phi-divergence test estimator for multinomial probabilities," Computational Statistics & Data Analysis, Elsevier, vol. 50(7), pages 1749-1773, April.


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