Estimation of Population Mean and Total in a Finite Population Setting Using Multiple Auxiliary Variables

This paper introduces a new sampling design in a finite population setting, where potential sampling units have a wealth of auxiliary information that can be used to rank them into partially ordered sets. The proposed sampling design selects a set of sampling units. These units are judgment ranked without measurement by using available auxiliary information. The ranking process allows ties among ranks whenever units cannot be ranked accurately with high confidence. The ranking information from all sources is combined in a meaningful way to construct strength-of-agreement weights. These weights are then used to select a single sampling unit for full measurement in each set. Three different levels of sampling design, level-0, level-1, and level-2, are investigated. They differ in their replacement policies. Level-0 sampling designs construct the sample by sampling with replacement, level-1 sampling designs constructs the sample without replacement of the fully measured unit in each set, and level-2 sampling designs construct the sample without replacement on the entire set. For these three designs, we estimate the first and second order inclusion probabilities and construct estimators for the population total and mean. We develop a bootstrap resampling procedure to estimate the variances of the estimators and to construct percentile confidence intervals for the population mean and total. We show that the new sampling designs provide a substantial amount of efficiency gain over their competitor designs in the literature.