On Stratification Using Auxiliary Variables and Discriminant Method

Abstract

Let U be a fixed population of size N from which a sample S of size n be drawn. We assume that values of variable Y are observed in the sample S and mean estimation is a goal of the survey. Moreover, let us assume that values of auxiliary variables X₁,…, X_m are known in the whole population. With fixed n, the mean should be estimated with an error as low as possible. Thus, the sample S selection method and an unbiased estimator with possible low variance should be established. A sampling strategy using auxiliary variables data may be an alternative to simply random sampling. The method proposed below depends on the selection of a preliminary sample S_p of size n_p (n_p < n) and next stratification of the remainder population and selection of a stratified sample S_s with size n_s.