Implications of survey design for generalized regression estimation of linear functions

Abstract

Abstract The paper presents a general randomization theory approach to point and interval estimation of Q linear functions Tq = ΣN1ckqYk(q = 1,…,Q), where Y1,…,YN are values of a variable of interest Y in a finite population. Such linear functions include population and domain means and totals, population regression coefficients, etc. We assume that some auxiliary information can be exploited. This suggests the generalized regression technique based on the fit of a linear model, whereby is created approximately design unbiased estimators Tq. The paper focuses on estimation of the variance-covariance matrix of the Tq for single stage and two stage designs. Two techniques based on Taylor expansions are compared. Results of Monte-Carlo experiments (not reported here) show that the coverage properties are good of normal-theory confidence intervals flowing from one or the other variance estimate.