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Estimation of order-restricted means of two normal populations under the LINEX loss function

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  • Tiefeng Ma
  • Shuangzhe Liu

Abstract

In this paper, the estimation of order-restricted means of two normal distributions is studied under the LINEX loss function, when the variances are unknown and possibly unequal. Under certain sufficient conditions to be described in this paper, the proposed plug-in estimators uniformly perform better than the existing unrestricted maximum likelihood estimators. Further, the restricted maximum likelihood estimators are compared with the unrestricted maximum likelihood estimators under the Pitman nearness criterion. A simulation study is conducted and it is shown that our proposed plug-in estimators perform better than the unrestricted maximum likelihood estimators. An illustrative example of real data analysis is also given to compare the estimators. Copyright Springer-Verlag 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:76:y:2013:i:3:p:409-425
    DOI: 10.1007/s00184-012-0396-6
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    References listed on IDEAS

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    1. M. Arashi & S. Tabatabaey, 2010. "Estimation of the location parameter under LINEX loss function: multivariate case," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(1), pages 51-57, July.
    2. Gamage, Jinadasa & Mathew, Thomas, 2008. "Inference on mean sub-vectors of two multivariate normal populations with unequal covariance matrices," Statistics & Probability Letters, Elsevier, vol. 78(4), pages 420-425, March.
    3. Srivastava, M.S. & Ehsanes Saleh, A.K.Md., 2005. "Estimation of the mean vector of a multivariate normal distribution: subspace hypothesis," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 55-72, September.
    4. 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.
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    Cited by:

    1. Tiefeng Ma & Shuangzhe Liu & S. Ahmed, 2014. "Shrinkage estimation for the mean of the inverse Gaussian population," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(6), pages 733-752, August.

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