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Estimation of a Finite Population Mean and Total Using Population Ranks of Sample Units

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  • Omer Ozturk

    (The Ohio State University)

Abstract

This paper introduces new estimators for population total and mean in a finite population setting, where ranks (or approximate ranks) of population units are available before selecting sample units. The proposed estimators require selecting a simple random sample and identifying the population ranks of sample units. Selection of the sample can be performed with- or without-replacement. The population ranks of the selected units of with-replacement samples are determined among all population units. On the other hand, the ranks of the sample units of without-replacement samples are identified in two different ways: (1) The rank of a sample unit is determined sequentially among the remaining population units after excluding all previously ranked sample units from the population; (2) The ranks are determined among all units in the population. By conditioning on these population ranks, we construct a set of weighted estimators, develop a bootstrap re-sampling procedure to estimate the variances of the estimators, and construct percentile confidence intervals for the population mean and total. We show that the new estimators provide a substantial amount of efficiency gain over their competitors. We apply the proposed estimators to estimate corn production in one of the counties in Ohio.

Suggested Citation

  • Omer Ozturk, 2016. "Estimation of a Finite Population Mean and Total Using Population Ranks of Sample Units," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(1), pages 181-202, March.
    • Handle: RePEc:spr:jagbes:v:21:y:2016:i:1:d:10.1007_s13253-015-0231-4
    DOI: 10.1007/s13253-015-0231-4
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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.
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    6. Jesse Frey & Omer Ozturk, 2011. "Constrained estimation using judgment post-stratification," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(4), pages 769-789, August.
    7. 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.
    8. Frey, Jesse & Feeman, Timothy G., 2012. "An improved mean estimator for judgment post-stratification," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 418-426.
    9. Jesse Frey & Timothy Feeman, 2013. "Variance estimation using judgment post-stratification," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 551-569, June.
    10. Xinlei Wang & Ke Wang & Johan Lim, 2012. "Isotonized CDF Estimation from Judgment Poststratification Data with Empty Strata," Biometrics, The International Biometric Society, vol. 68(1), pages 194-202, March.
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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.
    3. Omer Ozturk & Olena Kravchuk, 2021. "Judgment Post-stratified Assessment Combining Ranking Information from Multiple Sources, with a Field Phenotyping Example," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(3), pages 329-348, September.

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