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March, 1975 On a Class of Uniformly Admissible Estimators for Finite Populations
Rm. Sekkappan, M. E. Thompson
Ann. Statist. 3(2): 492-499 (March, 1975). DOI: 10.1214/aos/1176343078


Let $C'$ be a class of sampling designs of fixed expected sample size $n$ and fixed inclusion probabilities $\pi_i$ and $C$ be the subclass of $C'$ consisting of designs of fixed size $n$ and inclusion probabilities $\pi_i$. Then it is established that the pair $(e^\ast, p^\ast)$ where $p^\ast \in C$ and $e^\ast(x, \mathbf{x}) = \sigma_{i \in s} b_i x_i, b_1 > 1$, and $\sigma^N_1 (b_i)^{-1} = E(n(s)) = n$, is strictly uniformly admissible among pairs $(e_1, p_1)$ where $p_1 \in C'$ and $e_1$ is any measurable estimate.


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Rm. Sekkappan. M. E. Thompson. "On a Class of Uniformly Admissible Estimators for Finite Populations." Ann. Statist. 3 (2) 492 - 499, March, 1975.


Published: March, 1975
First available in Project Euclid: 12 April 2007

MathSciNet: MR359114
Digital Object Identifier: 10.1214/aos/1176343078

Keywords: 62 , D05 , finite populations , Horvitz-Thompson estimator , unequal probability sampling , uniform admissibility

Rights: Copyright © 1975 Institute of Mathematical Statistics

Vol.3 • No. 2 • March, 1975
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