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A note on sequential estimation of the size of a population under a general loss function

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  • Bai, Z. D.
  • Chow, Mosuk

Abstract

In estimating the size of a finite population under a sequential sampling scheme where the stopping rule is to stop sampling when a fixed number of marked items are observed, it has been shown that the maximum likelihood estimator (MLE) does not have an explicit expression and is inadmissible under weighted-squared-error loss. This note shows that the MLE is inadmissible under a very general class of loss functions. Also, a class of estimators which dominate the MLE is constructed and given in the article. Finally, an optimal class of estimators for some commonly used loss functions will be derived.

Suggested Citation

  • Bai, Z. D. & Chow, Mosuk, 2000. "A note on sequential estimation of the size of a population under a general loss function," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 159-164, April.
    • Handle: RePEc:eee:stapro:v:47:y:2000:i:2:p:159-164
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    References listed on IDEAS

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    1. Chow, Mosuk, 1990. "Admissibility of MLE for simultaneous estimation in negative binomial problems," Journal of Multivariate Analysis, Elsevier, vol. 33(2), pages 212-219, May.
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