Estimation of rare and clustered population variance in adaptive cluster sampling

Abstract

Many researchers used auxiliary information together with survey variable to improve the efficiency of population parameters like mean, variance, total and proportion. Ratio and regression estimation are the most commonly used methods that utilized auxiliary information in different ways to get the maximum benefits in the form of high precision of the estimators. Thompson first introduced the concept of Adaptive cluster sampling, which is an appropriate technique for collecting the samples from rare and clustered populations. In this article, a generalized exponential type estimator is proposed and its properties have been studied for the estimation of rare and highly clustered population variance using single auxiliary information. A numerical study is carried out on a real and artificial population to judge the performance of the proposed estimator over the competing estimators. It is shown that the proposed generalized exponential type estimator is more efficient than the adaptive and non adaptive estimators under conventional sampling design.

Keywords:

• Adaptive cluster sampling
• clustered population
• Hansen-Hurwitz estimation
• variance estimation
• exponential estimators

Acknowledgments

The first author is thankful to the Higher Education Commission (HEC) of Pakistan for awarding the International Research Support Initiative fellowship. The first author is grateful to the Editor In Chief for the extension in the deadline of the revised version of the article. The authors thank anonymous referees for their careful reading and constructive suggestions that led to improvement over an earlier version of the article.