Generalized estimator for the estimation of rare and clustered population variance in adaptive cluster sampling

ABSTRACT

Adaptive cluster sampling (ACS) is considered to be the most suitable sampling design for the estimation of rare, hidden, clustered and hard-to-reach population units. The main characteristic of this design is that it may select more meaningful samples and provide more efficient estimates for the field investigator as compare to the other conventional sampling designs. In this paper, we proposed a generalized estimator with a single auxiliary variable for the estimation of rare, hidden and highly clustered population variance under ACS design. The expressions of approximate bias and mean square error are derived and the efficiency comparisons have been made with other existing estimators. A numerical study is carried out on a real population of aquatic birds together with an artificial population generated by Poisson cluster process. Related results of numerical study show that the proposed generalized variance estimator is able to provide considerably better results over the competing estimators.

KEYWORDS:

• Adaptive cluster sampling
• auxiliary information
• clustered population
• Hansen–Hurwitz estimation
• Poisson clustered process

Acknowledgements

The authors are thankful to David. R. Smith and Cem Kadilar for the pre-review of the paper. The authors are grateful to the Editor-In-Chief, associate editor and anonymous referees for their careful reading and constructive suggestions that led to improvement over an earlier version of the article.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author is thankful to the Higher Education Commission (HEC) of Pakistan for awarding the International Research Support Initiative fellowship.