The authors deal with adaptive cluster sampling, a better alternative of the simple random sampling in cases when the population is rare and clustered. With this approach, auxiliary information is often used in order to overcome the problem with the increasing sample size.
A two-stage negative adaptive cluster sampling design is proposed as a combination of two-stage sampling and negative adaptive cluster sampling. In this design, an auxiliary variable which is highly negatively correlated with the variable of interest and auxiliary information is completely known.
In the first stage of this design, an initial random sample is drawn by using the auxiliary information. Further, networks in the population are discovered which serve as the primary-stage units (PSUs).
In the second stage, random samples of unequal sizes are drawn from the PSUs to get the secondary-stage units (SSUs).The values of the auxiliary variable and the variable of interest are recorded for these SSUs.
Regression estimator is proposed to estimate the population total of the variable of interest. A new estimator, Composite Horwitz-Thompson (CHT)-type estimator, is also proposed. It is based on only the information on the variable of interest. Variances of the above two estimators along with their unbiased estimators are derived.
Using this proposed methodology, sample survey was conducted at Western Ghat of Maharashtra, India. The comparison of the performance of these estimators and methodology is presented and compared with other existing methods. The cost-benefit analysis is given.