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Information content of partially rank-ordered set samples

Author

Listed:
  • Armin Hatefi

    (The Fields Institute for Research in Mathematical Sciences
    University of Toronto)

  • Mohammad Jafari Jozani

    (University of Manitoba)

Abstract

Partially rank-ordered set (PROS) sampling is a generalization of ranked set sampling in which rankers are not required to fully rank the sampling units in each set, hence having more flexibility to perform the necessary judgemental ranking process. The PROS sampling has a wide range of applications in different fields ranging from environmental and ecological studies to medical research and it has been shown to be superior over ranked set sampling and simple random sampling for estimating the population mean. We study Fisher information content and uncertainty structure of the PROS samples and compare them with those of simple random sample (SRS) and ranked set sample (RSS) counterparts of the same size from the underlying population. We study uncertainty structure in terms of the Shannon entropy, Rényi entropy and Kullback–Leibler (KL) discrimination measures.

Suggested Citation

  • Armin Hatefi & Mohammad Jafari Jozani, 2017. "Information content of partially rank-ordered set samples," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(2), pages 117-149, April.
    • Handle: RePEc:spr:alstar:v:101:y:2017:i:2:d:10.1007_s10182-016-0277-9
    DOI: 10.1007/s10182-016-0277-9
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    References listed on IDEAS

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    1. Barabesi, Lucio & El-Sharaawi, Abdel, 2001. "The efficiency of ranked set sampling for parameter estimation," Statistics & Probability Letters, Elsevier, vol. 53(2), pages 189-199, June.
    2. McIntyre, G.A., 2005. "A Method for Unbiased Selective Sampling, Using Ranked Sets," The American Statistician, American Statistical Association, vol. 59, pages 230-232, August.
    3. Zehua Chen & You-Gan Wang, 2004. "Efficient Regression Analysis with Ranked-Set Sampling," Biometrics, The International Biometric Society, vol. 60(4), pages 997-1004, December.
    4. Hatefi, Armin & Jafari Jozani, Mohammad, 2013. "Fisher information in different types of perfect and imperfect ranked set samples from finite mixture models," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 16-31.
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