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Pitman closeness of the class of isotonic estimators for ordered scale parameters of two Gamma distributions

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  • Tie Ma
  • Shuangzhe Liu

Abstract

The problem of estimating order-restricted scale parameters of two Gamma distributions is considered under the Pitman closeness criterion. A class of isotonic estimators including the MLE is proposed. Some properties of this class of isotonic estimators is given under the Pitman closeness criterion. In particular, some properties of the MLE naturally follow. We use simulation comparisons to examine the results. Copyright Springer-Verlag Berlin Heidelberg 2014

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  • 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.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:3:p:615-625
    DOI: 10.1007/s00362-013-0508-z
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    References listed on IDEAS

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    1. M. Özkale & Selahattin Kaçıranlar, 2008. "Comparisons of the r − k class estimator to the ordinary least squares estimator under the Pitman’s closeness criterion," Statistical Papers, Springer, vol. 49(3), pages 503-512, July.
    2. Yuan-Tsung Chang & Nobuo Shinozaki, 2002. "A Comparison of Restricted and Unrestricted Estimators in Estimating Linear Functions of Ordered Scale Parameters of Two Gamma Distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(4), pages 848-860, December.
    3. 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.
    4. Jafari Jozani, Mohammad & Davies, Katherine F. & Balakrishnan, Narayanaswamy, 2012. "Pitman closeness results concerning ranked set sampling," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2260-2269.
    5. Eshetu Wencheko, 2001. "Comparison of regression estimators using Pitman measures of nearness," Statistical Papers, Springer, vol. 42(3), pages 375-386, July.
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