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

✍ Scribed by Z.D. Bai; Mosuk Chow

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 78 KB
• Volume: 47
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(99)00152-2

✦ Synopsis

In estimating the size of a ÿnite population under a sequential sampling scheme where the stopping rule is to stop sampling when a ÿxed 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.