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