Two Stage Inverse Adaptive Cluster Sampling With Stopping Rule Depends upon the Size of Cluster

Abstract

When the population is rare and patchy, the traditional sampling designs provide the poor estimate of the population mean/total. In such situations adaptive sampling is useful. Also, the population is spread over a large geographical area, then it is divided into clusters and random sample of clusters is selected. The clusters so selected form a set of primary stage units (PSU’s). Further a random sample of units is selected from the selected clusters. They form a set of secondary stage units (SSU’s).This method is called as two-stage cluster sampling. In this article, we have proposed a new sampling design which is a combination of two stage inverse cluster sampling and adaptive cluster sampling designs (ACS). At the first stage, population is divided into non-overlapping clusters and a random sample of pre-fixed number of clusters is selected from these clusters. At the second stage, an initial sample of a fixed size is selected from each of these selected clusters. Further number of units satisfying some pre-determined condition (number of successes) is decided for each cluster. This number of successes depends upon the size of the cluster. If the initial sample from a cluster includes the required number of successes (non-zero units) then sampling is stopped and adaptation of neighbors is made. Otherwise sampling is continued till either the required number of successes are obtained or a pre-fixed upper bound for the number of units to be sampled from a cluster is attained. The estimator of population total at each stage is proposed by using Rao-Blackwellization procedure. Monte-Carlo study is presented for the sample survey of Western Ghat, India, to verify the efficiency of proposed design.