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December, 1986 Admissible Estimation of the Binomial Parameter $n$
S. M. Sadooghi-Alvandi
Ann. Statist. 14(4): 1634-1641 (December, 1986). DOI: 10.1214/aos/1176350185

Abstract

Suppose that $X$ has a binomial distribution $B(n, p)$, with known $p \in (0, 1)$ and unknown $n \in \{1, 2, \cdots\}$. A natural estimator for $n$ is given by $T(0) = 1, T(x) = x/p, x = 1, 2, \cdots$. This estimator is shown to be inadmissible under quadratic loss. It is shown that modifying $T(0)$ to $T(0) = -(1 - p)/(p \ln p)$ results in an admissible estimator. For $p \geq \frac{1}{2}$ it is further shown that this is the only admissible modification of $T(0)$. A partial result is also obtained for $p < \frac{1}{2}$.

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S. M. Sadooghi-Alvandi. "Admissible Estimation of the Binomial Parameter $n$." Ann. Statist. 14 (4) 1634 - 1641, December, 1986. https://doi.org/10.1214/aos/1176350185

Information

Published: December, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0615.62007
MathSciNet: MR868327
Digital Object Identifier: 10.1214/aos/1176350185

Subjects:
Primary: 62C30
Secondary: 62F20

Rights: Copyright © 1986 Institute of Mathematical Statistics

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Vol.14 • No. 4 • December, 1986
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