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

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  • Raosaheb V. Latpate

    (Savitribai Phule Pune University)

  • Jayant K. Kshirsagar

    (New Arts Commerce and Science College)

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.

Suggested Citation

  • Raosaheb V. Latpate & Jayant K. Kshirsagar, 2020. "Two Stage Inverse Adaptive Cluster Sampling With Stopping Rule Depends upon the Size of Cluster," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 70-83, May.
    • Handle: RePEc:spr:sankhb:v:82:y:2020:i:1:d:10.1007_s13571-018-0177-y
    DOI: 10.1007/s13571-018-0177-y
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    References listed on IDEAS

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    1. Arthur L. Dryver & Steven K. Thompson, 2005. "Improved unbiased estimators in adaptive cluster sampling," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 157-166, February.
    2. Mary C. Christman & Feng Lan, 2001. "Inverse Adaptive Cluster Sampling," Biometrics, The International Biometric Society, vol. 57(4), pages 1096-1105, December.
    3. E. Rocco, 2008. "Two-stage restricted adaptive cluster sampling," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 313-327.
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    Cited by:

    1. Rajesh Singh & Rohan Mishra, 2023. "Ratio-cum-product Type Estimators for Rare and Hidden Clustered Population," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 33-53, May.

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