Introduction to Variance Estimation

The book is organized in a way that emphasizes both the theory and applications of the various variance estimating techniques. Each technique is presented in a separate chapter, and each chapter divided into several main sections. The opening sections deal with the theory and motivation for the particular method of variance estimation. Results are often presented in the form of theorems; proofs are deleted when trivial or when a reference is readily available. The latter sections of each chapter present numerical examples where the particular technique was applied (and perhaps modified) to a real survey. The objectives of this organization format are to provide the student with a firm technical understanding of the methods of variance estimation; to stimulate further research on the various techniques, particularly as they apply to large, complex surveys; and to provide an easy reference for the survey researcher who is faced with the problem of estimating variances for real survey data.

Résumé

From the reviews:

"The main purpose of this book is to describe a number of techniques for variance estimation that have been suggested in recent years, and to demonstrate how they may be used in the context of modern complex sample surveys. The various techniques to be described are widely scattered through the statistical literature; currently, there is no systematic treatment of this methodology that brings together the state of the art in one manuscript. The book accomplishes this objective." (Dmitry Ostrouchov, Zentralblatt MATH, Vol. 1050, 2005)

Contenu
The Method of Random Groups.- Variance Estimation Based on Balanced Half-Samples.- The Jackknife Method.- The Bootstrap Method.- Taylor Series Methods.- Generalized Variance Functions.- Variance Estimation for Systematic Sampling.- Summary of Methods for Complex Surveys.- Hadamard Matrices.- Asymptotic Theory of Variance Estimators.- Transformations.- The Effect of Measurement Errors on Variance Estimation.- Computer Software for Variance Estimation.- The Effect of Imputation on Variance Estimation.