Precision enhancement in variance estimation for complex environmental populations using adaptive cluster sampling

Estimating dispersion in populations that are extremely rare, hidden, geographically clustered, and hard to access is a well-known challenge. Conventional sampling approaches tend to overestimate the variance, even though it should be genuinely reduced. In this environment, adaptive cluster sampling is considered to be the most efficient sampling technique as it provides generally a lower variance than the other conventional probability sampling designs for the assessment of rare and geographically gathered population parameters like mean, total, variance, etc. The use of auxiliary data is very common to obtain the precise estimates of the estimators by taking advantage of the correlation between the survey variable and the auxiliary data. In this article, we introduced a generalized estimator for estimating the variance of populations that are rare, hidden, geographically clustered and hard-to-reached. The proposed estimator leverages both actual and transformed auxiliary data through adaptive cluster sampling. The expressions of approximate bias and mean square error of the proposed estimator are derived up to the first-order approximation using Taylor expansion. Some special cases are also obtained using the known parameters associated with the auxiliary variable. The proposed class of estimators is compared with available estimators using simulation and real data applications.