Optimal Regression Estimator for Stratified Two-Stage Sampling
Regression estimators are often used in survey sampling for point estimation. We propose a new regression estimator based upon the optimal estimator proposed by Berger et al., (2003). The proposed estimator can be used for stratified two-stage sampling designs when the sampling fraction is negligible and the primary sampling units (PSU) are selected with unequal probabilities. For example, this is the case for self-weighted two-stage designs. We assume that we have auxiliary variables available for the secondary sampling units (SSU) and the primary sampling units (PSU). We propose to use an ultimate cluster approach to estimate the regression coefficient of the regression estimator. Estevao and Särndal (2006) proposed a regression estimator for two-stage sampling. This estimator will be compared with the proposed estimator through a simulation study. We will show that the proposed estimator is more accurate that the Estevao and Särndal (2006) estimator when the strata are homogeneous.
KeywordsDesign-based approach Horvitz–Thompson estimator Stratification Ultimate cluster approach Unequal inclusion probabilities
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