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Inclusion probabilities in partially rank ordered set sampling

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  • Ozturk, Omer
  • Jafari Jozani, Mohammad

Abstract

In a finite population setting, this paper considers a partially rank ordered set (PROS) sampling design. The PROS design selects a simple random sample (SRS) of M units without replacement from a finite population and creates a partially rank ordered judgment subsets by dividing the units in SRS into subsets of a pre-specified size. The subsetting process creates a partial ordering among units in which each unit in subset h is considered to be smaller than every unit in subset h′ for h′>h. The PROS design then selects a unit for full measurement from one of these subsets. Remaining units are returned to the population based on three replacement policies. For each replacement policy, we compute the first and second order inclusion probabilities and use them to construct the Horvitz–Thompson estimator and its variance for the estimation of the population total and mean. It is shown that the replacement policy that does not return any of the M units, prior to selection of the next unit for full measurement, outperforms all other replacement policies.

Suggested Citation

  • Ozturk, Omer & Jafari Jozani, Mohammad, 2014. "Inclusion probabilities in partially rank ordered set sampling," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 122-132.
    • Handle: RePEc:eee:csdana:v:69:y:2014:i:c:p:122-132
    DOI: 10.1016/j.csda.2013.07.034
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    References listed on IDEAS

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    1. M. Al-Saleh & H. Samawi, 2007. "A note on inclusion probability in ranked set sampling and some of its variations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 198-209, May.
    2. G. Patil & A. Sinha & C. Taillie, 1995. "Finite population corrections for ranked set sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(4), pages 621-636, December.
    3. 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.
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    Cited by:

    1. Omer Ozturk, 2019. "Post-stratified Probability-Proportional-to-Size Sampling from Stratified Populations," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(4), pages 693-718, December.
    2. Omer Ozturk, 2019. "Two-stage cluster samples with ranked set sampling designs," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(1), pages 63-91, February.

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