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Estimation of means of multivariate normal populations with order restriction

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  • Ma, Tiefeng
  • Wang, Songgui

Abstract

Multivariate isotonic regression theory plays a key role in the field of statistical inference under order restriction for vector valued parameters. Two cases of estimating multivariate normal means under order restricted set are considered. One case is that covariance matrices are known, the other one is that covariance matrices are unknown but are restricted by partial order. This paper shows that when covariance matrices are known, the estimator given by this paper always dominates unrestricted maximum likelihood estimator uniformly, and when covariance matrices are unknown, the plug-in estimator dominates unrestricted maximum likelihood estimator under the order restricted set of covariance matrices. The isotonic regression estimators in this paper are the generalizations of plug-in estimators in unitary case.

Suggested Citation

  • Ma, Tiefeng & Wang, Songgui, 2010. "Estimation of means of multivariate normal populations with order restriction," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 594-602, March.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:3:p:594-602
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    References listed on IDEAS

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    1. Shi, Ning-Zhong & Jiang, Hua, 1998. "Maximum Likelihood Estimation of Isotonic Normal Means with Unknown Variances," Journal of Multivariate Analysis, Elsevier, vol. 64(2), pages 183-195, February.
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    Cited by:

    1. Tiefeng Ma & Shuangzhe Liu, 2013. "Estimation of order-restricted means of two normal populations under the LINEX loss function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(3), pages 409-425, April.
    2. Tie Ma & Shuangzhe Liu, 2014. "Pitman closeness of the class of isotonic estimators for ordered scale parameters of two Gamma distributions," Statistical Papers, Springer, vol. 55(3), pages 615-625, August.

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