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Maximum Likelihood Estimation of Means and Variances from Normal Populations Under Simultaneous Order Restrictions

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  • Shi, N. Z.

Abstract

For k normal populations with unknown means [mu]i and unknown variances [sigma]2i, i = 1, ..., k, assume that there are some order restrictions among the means and variances, respectively, for example, simple order restrictions: [mu]1 = [sigma]22 >= ... >= [sigma]2k > 0. Some properties of maximum likelihood estimation of [mu]is and [sigma]2i are discussed and an algorithm of obtaining the maximum likelihood estimators under the order restrictions is proposed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:50:y:1994:i:2:p:282-293
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    Cited by:

    1. Mondal, Anjana & Sattler, Paavo & Kumar, Somesh, 2023. "Testing against ordered alternatives in a two-way model without interaction under heteroscedasticity," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    2. 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.
    3. 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.
    4. Jamshidian, Mortaza, 2004. "On algorithms for restricted maximum likelihood estimation," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 137-157, March.
    5. Shi, Ning-Zhong & Zheng, Shu-Rong & Guo, Jianhua, 2005. "The restricted EM algorithm under inequality restrictions on the parameters," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 53-76, January.
    6. Yuan-Tsung Chang & Nobuo Shinozaki, 2015. "Estimation of two ordered normal means under modified Pitman nearness criterion," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(5), pages 863-883, October.

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