Statistical matching. A frequentist theory, practical applications, and alternative Bayesian approaches
The first chapter gives an `Introduction' into statistical matching, the task to put together different data sources with the help of some common variables. Chapter two points out the basic principles of statistical matching in detail. This chapter develops a `Frequentist Theory of Statistical Matching'. The theory allows to analyze the properties of the matching process systematically. It is explained how conditional independence is established by traditional statistical matching techniques. The last section concerns conditional independence in general, and some simulation studies are presented. An overview of the roots and history of statistical matching and its applications is given in chapter three, `Practical Applications of Statistical Matching'. Some of the most popular matching techniques used in Germany and other countries are described. Chapter four, entitled `Alternative Approaches to Statistical Matching', is the core chapter of the book. Here multiple imputation is introduced as proposed by \textit{D. B. Rubin} [see J. Am. Stat. Assoc. 91, No. 434, 473-489 (1996; Zbl 0869.62014)]. Notational preliminaries concerning the treatment of missing data in general as well as statistical matching in particular are presented. Principles of Bayesian argumentation are explained and imputation techniques such as data augmentation and iterative univariate imputations based on Markov chain Monte Carlo methods are discussed. A new noniterative multivariate imputation method is derived successively. The use of prior information is discussed in detail to estimate bounds of the unconditional association. Finally, the alternative approaches proposed are compared by means of a simulation study. Chapter five gives an `Empirical Evaluation of Alternative Approaches'. The practical importance of the alternative methods proposed is shown in this chapter. The next one gives a `Synopsis and Outlook'. The main S-Plus routines developed in this book are listed in the appendix.
scientific article; zbMATH DE number 1817061