## The Annals of Statistics

- Ann. Statist.
- Volume 5, Number 2 (1977), 414-418.

### Convex Sets of Finite Population Plans

#### Abstract

Let $P_1$ be a finite population sampling plan and $V$ a collection of subsets of units. The inclusion probabilities for members of $V$ may be calculated. For example, if $V$ comprises all single units and pairs of units we obtain all first and second order inclusion probabilities $\pi_i, \pi_{ij}$. Another plan $P_2$ is called equivalent to $P_1$ with respect to $V$ if the corresponding inclusion probabilities for $P_1$ are equal to those for $P_2$. However, $P_2$ may have fewer samples with positive probability of selection, that is to say smaller "support." An upper bound is put on the minimum support size of all such $P_2$. For $P_1$ simple random sampling, some examples are given for $P_2$ with small support.

#### Article information

**Source**

Ann. Statist., Volume 5, Number 2 (1977), 414-418.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176343809

**Digital Object Identifier**

doi:10.1214/aos/1176343809

**Mathematical Reviews number (MathSciNet)**

MR518633

**Zentralblatt MATH identifier**

0365.62012

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62D05: Sampling theory, sample surveys

**Keywords**

Finite populations survey sampling convexity randomization

#### Citation

Wynn, H. P. Convex Sets of Finite Population Plans. Ann. Statist. 5 (1977), no. 2, 414--418. doi:10.1214/aos/1176343809. https://projecteuclid.org/euclid.aos/1176343809