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

*Raosaheb V. Latpate* () and
*Jayant K. Kshirsagar* ()

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Raosaheb V. Latpate: Savitribai Phule Pune University

Jayant K. Kshirsagar: New Arts Commerce and Science College

*Sankhya B: The Indian Journal of Statistics*, 2020, vol. 82, issue 1, No 3, 70-83

**Abstract:**
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.

**Keywords:** Adaptive cluster sampling (ACS); two stage sampling; general inverse adaptive sampling; sequential sampling; two stage estimator.; Primary 62; Secondary D05. (search for similar items in EconPapers)

**Date:** 2020

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**DOI:** 10.1007/s13571-018-0177-y

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