### 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.

Original language | English (US) |
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Pages (from-to) | 159-164 |

Number of pages | 6 |

Journal | Statistics and Probability Letters |

Volume | 47 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1 2000 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

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*Statistics and Probability Letters*, vol. 47, no. 2, pp. 159-164. https://doi.org/10.1016/S0167-7152(99)00152-2

**A note on sequential estimation of the size of a population under a general loss function.** / Bai, Z. D.; Chow, Mosuk.

Research output: Contribution to journal › Article

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

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

VL - 47

SP - 159

EP - 164

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

IS - 2

ER -