Negative adaptive cluster sampling

Abstract

The traditional sampling methods such as simple random sampling, stratified sampling etc. cannot be used to study the rare and clustered populations. Such type of populations are frequently observed in ecological, environmental and social sciences. In such situations, often the auxiliary information is collected along with the variable of interest. Obviously, one would like to exploit this auxiliary information to the maximum extent. We consider an auxiliary variable which is highly negatively correlated with the variable of interest. An initial random sample of a fixed size is drawn from the population under study. Further, networks are formed around the units selected in this sample that satisfy the pre specified condition with respect to the auxiliary variable. We used the procedure given by Thompson (1990) for that purpose. The variable of interest is measured corresponding to the units included in these networks. In such situation, negative adaptive cluster sampling (NACS) is of more practical interest than that of the conventional sampling designs. NACS can provide more informative sample for the investigator and more efficient estimates of the population parameters of interest. The parameters of the population are estimated by using the information on the variable of interest corresponding to the units included in the different networks. Different estimators are proposed in this article for the population total of the interest variable. The performance of these estimators is compared by using the data collected from a pilot study by using NACS method.