<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Rejective sampling was first introduced by Hájek in 1964 as a way to select a sample consisting uniquely of distinct units. If <italic>n</italic> denotes the fixed sample size, the <italic>n</italic> units are drawn independently with probabilities that may vary from unit to unit and the samples in which all units are not distinct are rejected. More generally, in rejective sampling, we select repeated samples according to a basic sampling design until a selected sample meets a specified balancing tolerance. Given a set of auxiliary variables, we consider a procedure in which the probability sample is rejected unless the sample mean of the auxiliary variables is within a specified distance of its corresponding population mean. The procedure represents an alternative to the well-known balanced cube method. In this article, we propose an estimator of the variance under the rejective sampling design. We also present the results of a Monte Carlo simulation study.</p></abstract>

Rejective sampling was first introduced by Hájek in 1964 as a way to select a sample consisting uniquely of distinct units. If n denotes the fixed sample size, the n units are drawn independently with probabilities that may vary from unit to unit and the samples in which all units are not distinct are rejected. More generally, in rejective sampling, we select repeated samples according to a basic sampling design until a selected sample meets a specified balancing tolerance. Given a set of auxiliary variables, we consider a procedure in which the probability sample is rejected unless the sample mean of the auxiliary variables is within a specified distance of its corresponding population mean. The procedure represents an alternative to the well-known balanced cube method. In this article, we propose an estimator of the variance under the rejective sampling design. We also present the results of a Monte Carlo simulation study.

A Procedure for Estimating the Variance of the Population Mean in Rejective Sampling

Journal of Official Statistics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Rejective sampling was first introduced by Hájek in 1964 as a way to select a sample consisting uniquely of distinct units. If n denotes the fixed sample size,...

A Procedure for Estimating the Variance of the Population Mean in Rejective Sampling

Published Online: Mar 17, 2020

Page range: 173 - 196

Received: Jun 01, 2018

Accepted: Jun 01, 2019

DOI: https://doi.org/10.2478/jos-2020-0009

Keywords
Balanced sampling, rejective sampling, normality assumption

© 2020 Marius Stefan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

A Procedure for Estimating the Variance of the Population Mean in Rejective Sampling

Published Online: Mar 17, 2020

Page range: 173 - 196

Received: Jun 01, 2018

Accepted: Jun 01, 2019

DOI: https://doi.org/10.2478/jos-2020-0009

KeywordsBalanced sampling, rejective sampling, normality assumption

© 2020 Marius Stefan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Balanced sampling, rejective sampling, normality assumption