Estimation of a finite population mean and total using population ranks of sample units. (English) Zbl 1342.62178
Summary: 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.
MSC:
| 62P12 | Applications of statistics to environmental and related topics |
| 62D05 | Sampling theory, sample surveys |
Keywords:
finite population; Horvitz-Thompson estimator; inclusion probabilities; coefficient of variation; ranked set sampling; judgment post stratified samplingReferences:
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