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

Z. D. Bai and Mosuk Chow

Statistics & Probability Letters, 2000, vol. 47, issue 2, 159-164

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.

Keywords: Admissibility; Capture-recapture; Maximum; likelihood; estimator; Sequential; sampling; Loss; function; Risk; function (search for similar items in EconPapers)
Date: 2000
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