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Minimax estimation of means of multivariate normal mixtures

Author

Listed:
  • Chou, Jine-Phone
  • Strawderman, William E.

Abstract

Assume X = (X1, ..., Xp)' is a normal mixture distribution with density w.r.t. Lebesgue measure, , where [Sigma] is a known positive definite matrix and F is any known c.d.f. on (0, [infinity]). Estimation of the mean vector under an arbitrary known quadratic loss function Q([theta], a) = (a - [theta])' Q(a - [theta]), Q a positive definite matrix, is considered. An unbiased estimator of risk is obatined for an arbitrary estimator, and a sufficient condition for estimators to be minimax is then achieved. The result is applied to modifying all the Stein estimators for the means of independent normal random variables to be minimax estimators for the problem considered here. In particular the results apply to the Stein class of limited translation estimators.

Suggested Citation

  • Chou, Jine-Phone & Strawderman, William E., 1990. "Minimax estimation of means of multivariate normal mixtures," Journal of Multivariate Analysis, Elsevier, vol. 35(2), pages 141-150, November.
    • Handle: RePEc:eee:jmvana:v:35:y:1990:i:2:p:141-150
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    Citations

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    Cited by:

    1. Fourdrinier, Dominique & Lemaire, Anne-Sophie, 2002. "Estimation under l1-Symmetry," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 303-323, November.
    2. Dominique Fourdrinier & Tatsuya Kubokawa & William E. Strawderman, 2023. "Shrinkage Estimation of a Location Parameter for a Multivariate Skew Elliptic Distribution," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 808-828, February.
    3. Fourdrinier Dominique & Lemaire Anne-Sophie, 2000. "ESTIMATION OF THE MEAN OF A e1-EXPONENTIAL MULTIVARIATE DISTRIBUTION," Statistics & Risk Modeling, De Gruyter, vol. 18(3), pages 259-274, March.

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