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Maximum Likelihood Estimation of Isotonic Normal Means with Unknown Variances


  • Shi, Ning-Zhong
  • Jiang, Hua


To analyze the isotonic regression problem for normal means, it is usual to assume that all variances are known or unknown but equal. This paper then studies this problem in the case that there are no conditions imposed on the variances. Suppose that we have data drawn fromkindependent normal populations with unknown means[mu]i's and unknown variances[sigma]2i's, in which the means are restricted by a given partial ordering. This paper discusses some properties of the maximum likelihood estimates of[mu]i's and[sigma]2i's under the restriction and proposes an algorithm for obtaining the estimates.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:jmvana:v:64:y:1998:i:2:p:183-195

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    References listed on IDEAS

    1. Shi, N. Z., 1994. "Maximum Likelihood Estimation of Means and Variances from Normal Populations Under Simultaneous Order Restrictions," Journal of Multivariate Analysis, Elsevier, vol. 50(2), pages 282-293, August.
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    Cited by:

    1. Hoferkamp, Carol & Das Peddada, Shyamal, 2002. "Parameter Estimation in Linear Models with Heteroscedastic Variances Subject to Order Restrictions," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 65-87, July.
    2. Jamshidian, Mortaza, 2004. "On algorithms for restricted maximum likelihood estimation," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 137-157, March.
    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. Tao, Jian & Shi, Ning-Zhong & Guo, Jianhua & Gao, Wei, 2002. "Stepwise procedures for the identification of minimum effective dose with unknown variances," Statistics & Probability Letters, Elsevier, vol. 57(2), pages 121-131, April.


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