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Order restricted estimators: some bias results

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  • Sampson, Allan R.
  • Singh, Harshinder
  • Whitaker, Lyn R.

Abstract

Stimulated by practical concerns in the use of order restricted estimators, we study some bias issues of isotonic estimators of ordered parameters. We obtain explicit expressions for biases of order restricted estimators of ordered means of two normal populations with common variance. Based on intuitive considerations, we also propose a new estimator of the common variance of two normal populations having ordered normal means and show that it has smaller bias than the maximum likelihood estimator of the variance and has smaller mean squared error than the usual unbiased estimator of the common variance.

Suggested Citation

  • Sampson, Allan R. & Singh, Harshinder & Whitaker, Lyn R., 2003. "Order restricted estimators: some bias results," Statistics & Probability Letters, Elsevier, vol. 61(3), pages 299-308, February.
    • Handle: RePEc:eee:stapro:v:61:y:2003:i:3:p:299-308
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    References listed on IDEAS

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    1. Amarjot Kaur & Harshinder Singh, 1991. "On the estimation of ordered means of two exponential populations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(2), pages 347-356, June.
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    Cited by:

    1. Rueda, Cristina, 2013. "Degrees of freedom and model selection in semiparametric additive monotone regression," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 88-99.

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