Model-based prediction of finite population totals

This chapter describes the idea of balanced samples and shows that BLUP of total based on models fulfilling certain conditions are bias-robust in weighted balanced samples. One of the practical constraints in many survey applications is that a sample that is selected to be balanced does not remain so at the analysis stage. Losses due to non-response and ineligible units can destroy balance. Deviations of the working model from models that might be better descriptions of the population values are a concern when estimating the variance. If the variance structure assumed in the working model is wrong, standard least squares variance estimators are vulnerable to bias. Many naturally occurring populations exhibit clustering in which units that are, in some sense, near each other have similar characteristics. Households in the same neighborhood may tend to have similar incomes, education levels of the heads of household, and amounts of expenditures on food and clothing. A population of school districts, schools within districts, classes within schools, and students within classes is an example.