TY - JOUR

T1 - A note on sequential estimation of the size of a population under a general loss function

AU - Bai, Z. D.

AU - Chow, Mosuk

N1 - Funding Information:
The work of the second author was partially supported by the NSF Grant DMS 97-09481. We want to thank Professor George A.F. Seber and Professor Duncan K.H. Fong for their helpful comments.

PY - 2000/4/1

Y1 - 2000/4/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0041777841&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041777841&partnerID=8YFLogxK

U2 - 10.1016/S0167-7152(99)00152-2

DO - 10.1016/S0167-7152(99)00152-2

M3 - Article

AN - SCOPUS:0041777841

SN - 0167-7152

VL - 47

SP - 159

EP - 164

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 2

ER -