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.
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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 -