On variance estimation for the two-phase regression estimator

Abstract: Regression estimation under two-phase sampling is a cost-effective technique for estimating a finite population total. This dissertation consists of four papers, summarized in an introductory chapter, all of which focus on the use of auxiliary information in estimating the variance of the generalted regression estimator under two-phase sampling.The first paper deals with the analysis of results from so-called computersimulation experiments for policy analysis. In particular, we consider applications based on input from the National Resources Inventory, which is a stratified two-stage area sample of nonfederal land in the United States. The estimation problem is formulated in terms of generalised two-phase regression estimation, and a variance estimation strategy is developed.In the second paper, a new approach to variance estimation is suggested. Compared with the reference estimators considered, the new approach, which may be seen as a generalisation of the approach used in paper one, makes more extensive use of the available auxiliary information, and hence it may be expected to be more efficient.Yet another approach to variance estimation is discussed in the third paper. Although conceptually different from the approach discussed in the second paper, it yields very similar results when applied to the generalized regression estimator under two-phase sampling. The approach may readily be extended to allow for variance estimation under multi-phase sampling.The fourth paper, finally, deals with jackknife variance estimation. Twoestimators of potential practical interest are derived, and the estimators are compared empirically by means of a small-scale Monte Carlo study.