This book gives a concise presentation of commonly accepted theoretical models in sampling theory. In Chapter 1, classical unified theory is discussed and a series of new concepts is introduced as well as procedures of special importance. Among them is the discussion of the estimation equation approach which is introduced with elegance and its implications for the selection of sampling strategies are fixed. This is the first complete exposition of this theme in a sampling theory book. The second chapter gives a complete account of the main sampling strategies of common use in practice. The third chapter is dedicated to a similar task within the predictive approach. It is worthy to mention the discussion of the role of James-Stein estimation within this theoretical frame.
Chapter 4 is devoted to the study of different asymptotic approaches. The problem of variance estimation is tackled in Chapter 5 introducing the analysis of jacknife techniques. The following chapter is devoted to the exposition of models in multistage and multiphase sampling. This set of chapters is recommended for a high-mathematical-level course on sampling. The use of other standard books, as W. G. Cochran, Sampling techniques. 3rd ed. (1977; Zbl 0353.62011), can be used for complementing some aspects of practical interest.
The rest of the chapters gives interesting results close to practical problems. They are discussed at a similar theoretical level as the preceding ones. Chapter 7 should be specially important because it includes recent results on the use of intensive computation methods for estimating sampling errors in complex samples. The introduction of computing experiments would complete my personal expectations for the treatment of the subject.
The use of inadequate frames is thoroughly discussed. This theme is a common lack in current books. Chapter 9 gives a contemporary view of the general problem of using sampling for analytical purposes. The monograph of the first author and R. Mukerjee, Randomized response. Theory and techniques. (1988), is condensed in Chapter 10 and, as classic, the non-response problem receives a less complete treatment than the other subjects of the book.
Another remarkable aspect is that the number of references is not very large. The authors fixed the key references to the discussed results avoiding the usual mess of the search of the seminal papers of a certain idea. This book fulfills the unsourmountable goal of providing an obligatory reference for sample surveyers and other related statisticians.