Efficient Estimators with Simple Variance in Unequal Probability Sampling

Abstract

Abstract For unequal probability sampling designs, design-based variance estimation is cumbersome because it requires second-order inclusion probabilities. For most fixed sample size probability proportional-to-size (φPS) schemes, these probabilities are difficult to compute, and the variance estimation depends on them for a tedious double-sum calculation. We show how to replace the traditional φPS scenario with simpler design/estimator alternatives that preserve the high efficiency characteristic of φPS schemes. These use the generalized regression estimator, and the variance estimation entails only the calculation of a simple weighted squared residual sum.