## The Annals of Statistics

### On a Class of Uniformly Admissible Estimators for Finite Populations

#### 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.

#### Article information

Source
Ann. Statist., Volume 3, Number 2 (1975), 492-499.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176343078

Digital Object Identifier
doi:10.1214/aos/1176343078

Mathematical Reviews number (MathSciNet)
MR359114

JSTOR