## The Annals of Statistics

- Ann. Statist.
- Volume 11, Number 3 (1983), 959-969.

### Asymptotic Theory of Systematic Sampling

#### Abstract

The main purpose of this paper is the development of an asymptotic theory of systematic sampling from a stochastic population. The superpopulation model assumed is that the population arises from a second-order stationary process. A comparison among the multiple random start systematic sampling schemes is made in terms of the limiting expected variance of the sample mean. Asymptotic normality of the systematic sampling mean is obtained, both unconditionally and conditionally on the given population. Finally, the asymptotic behavior of confidence intervals based on two distinct variance estimators is studied.

#### Article information

**Source**

Ann. Statist., Volume 11, Number 3 (1983), 959-969.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176346261

**Digital Object Identifier**

doi:10.1214/aos/1176346261

**Mathematical Reviews number (MathSciNet)**

MR707945

**Zentralblatt MATH identifier**

0519.62005

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62D05: Sampling theory, sample surveys

Secondary: 62F25: Tolerance and confidence regions 62E20: Asymptotic distribution theory

**Keywords**

Multiple random start systematic sampling limiting expected variance asymptotic normality variance estimator

#### Citation

Iachan, Ronaldo. Asymptotic Theory of Systematic Sampling. Ann. Statist. 11 (1983), no. 3, 959--969. doi:10.1214/aos/1176346261. https://projecteuclid.org/euclid.aos/1176346261