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

Omer Ozturk ()
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Omer Ozturk: The Ohio State University

Journal of Agricultural, Biological and Environmental Statistics, 2016, vol. 21, issue 1, No 11, 202 pages

Abstract: 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.

Keywords: Finite population; Horvitz–Thompson estimator; Inclusion probabilities; Coefficient of variation; Ranked set sampling; Judgment post stratified sampling (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s13253-015-0231-4

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