Rare and clustered population estimation using the adaptive cluster sampling with some robust measures

ABSTRACT

The use of robust measures helps to increase the precision of the estimators, especially for the estimation of extremely skewed distributions. In this article, a generalized ratio estimator is proposed by using some robust measures with single auxiliary variable under the adaptive cluster sampling (ACS) design. We have incorporated tri-mean (TM), mid-range (MR) and Hodges-Lehman (HL) of the auxiliary variable as robust measures together with some conventional measures. The expressions of bias and mean square error (MSE) of the proposed generalized ratio estimator are derived. Two types of numerical study have been conducted using artificial clustered population and real data application to examine the performance of the proposed estimator over the usual mean per unit estimator under simple random sampling (SRS). Related results of the simulation study show that the proposed estimators provide better estimation results on both real and artificial population over the competing estimators.

KEYWORDS:

• Adaptive cluster sampling
• Hansen–Hurwitz estimation
• simulated population
• expected sample size
• within-network variance

2010 Mathematics Subject Classification:

• 62D05

Acknowledgement

The first author is deeply thankful to Dr Muhammad Azam for his precious advices in R-programming. Additional thanks to the Editors-in-Chief and the anonymous reviewers for their valuable comments and suggestions, which substantially improved of the article.

Disclosure statement

No potential conflict of interest was reported by the authors.