Jan Wretman

Model Assisted Survey Sampling.

PART I: Principles of Estimation for Finite Populations and Important Sampling Designs: Survey Sampling in Theory and Practice. Basic Ideas in Estimation from Probability Samples. Unbiased Estimation for Element Sampling Designs. Unbiased Estimation for Cluster Sampling and Sampling in Two or More Stages. Introduction to More Complex Estimation Problems.- PART II: Estimation through Linear Modeling, Using Auxiliary Variables: The Regression Estimator. Regression Estimators for Element Sampling Designs. Regression Estimators for Cluster Sampling and Two-Stage Sampling.- PART III: Further Questions in Design and Analysis of Surveys: Two-Phase Sampling. Estimation for Domains. Variance Estimation. Searching for Optimal Sampling Designs. Further Statistical Techniques for Survey Data.- PART IV: A Broader View of Errors in Surveys: Nonsampling Errors and Extensions of Probability Sampling Theory. Nonresponse. Measurement Errors. Quality Declarations for Survey Data.- Appendix A - D.- References.

Regression analysis and ratio analysis for domains: A randomization-theory approach*

In most surveys, inference for domains poses a difficult problem because of data shortage. This paper presents a probability sampling theory approach to some common types of statistical analysis for domains of a surveyed population. Simple and multiple regression analysis, and analysis of ratios are considered. Two new methods are constructed and explored which can improve substantially over the common method based on sample-weighted sums of squares and products. These new methods use auxiliary variables whose importance depends on the extent to which they succeed in explaining certain patterns in the regression residuals. The theoretical conclusions are supported by empirical results from Monte Carlo experiments.