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