David A. Binder

Use of Estimating Functions for Estimation from Complex Surveys

Abstract We describe a method for point and interval estimation of population parameters from complex surveys using estimating functions. The theory was originally developed for infinite populations and has recently been applied to finite populations. With estimating functions, a unifying framework can be given for point and interval estimation of both finite and infinite population parameters. We discuss test inversion methods to derive confidence intervals for one-dimensional parameters and propose a method for eliminating nuisance parameters in the multidimensional setting. We show that special cases of our proposal result in conditional and orthogonal methods proposed in the literature. We describe a simulation study using real data to compare the coverage probabilities of confidence intervals obtained under various approaches.

Variance estimation for two-phase stratified sampling

The authors consider variance estimation for the generalized regression estimator in a two-phase context when the first-phase sample has been restratified using information gathered from the first-phase sample. Simple computational expressions for variance estimation are provided for the double expansion estimator and the reweighted expansion estimator of Kott & Stukel (1997). These estimators are compared using data from the Canadian Retail Commodity Survey.

Design- and Model-Based Inference for Model Parameters

Publisher Summary This chapter discusses the issues associated with making inferences about model parameters from survey data that have been obtained from a probability–sampling scheme using a frequency-based framework. In sample surveys, information is collected from a sample of units from a finite population. It is common for the sampling plan to be complex, which is defined as any sampling plan where the units are selected using a design that is not simple random sampling. When a survey is conducted, the survey producer targets a particular population of inference or a particular set of populations of inference. It is important to distinguish between two types of populations: the survey population and the target populations. It is presumed that the realizations of the random variables generated by such a model have given rise to the values of the characteristics of interest in the finite population from which the sample was selected. The relationship between the units of a population and the units of analysis is important. The researcher must be aware of the differences between the two types of units.