## The Annals of Statistics

- Ann. Statist.
- Volume 7, Number 2 (1979), 395-399.

### A Minimax Approach to Randomization and Estimation in Survey Sampling

#### Abstract

We consider a finite set of units, a population. With each unit is associated a real value (unknown to us) and a label (identifying the unit). Based on the labels we may select a sample, i.e., a subset of the population, to estimate the mean of the real values. In simple random sampling (not necessarily of fixed size) the selection probabilities of all samples are not affected by a permutation of the labels. It is assumed that we have to choose both a sampling design and a linearly invariant estimator, i.e., a linear function of the observed values with the property: equality of the observed values implies that the estimate is equal to this common value. Under these conditions we should use simple random sampling together with the sample mean as an estimator. This follows from the minimax criterion.

#### Article information

**Source**

Ann. Statist., Volume 7, Number 2 (1979), 395-399.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176344622

**Digital Object Identifier**

doi:10.1214/aos/1176344622

**Mathematical Reviews number (MathSciNet)**

MR520248

**Zentralblatt MATH identifier**

0399.62007

**JSTOR**

links.jstor.org

**Subjects**

Primary: 65D05: Interpolation

Secondary: 62K05: Optimal designs

**Keywords**

Finite populations simple random sampling and symmetric estimation modified minimax principle of Wesler simultaneous application to randomization and estimation

#### Citation

Stenger, H. A Minimax Approach to Randomization and Estimation in Survey Sampling. Ann. Statist. 7 (1979), no. 2, 395--399. doi:10.1214/aos/1176344622. https://projecteuclid.org/euclid.aos/1176344622