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Model assisted survey sampling. (English) Zbl 0742.62008
Springer Series in Statistics. New York etc.: Springer-Verlag. xv, 694 p. (1992).
The book is divided into four parts. The first part (5 chapters, 213 pp.) discusses the basic ideas of estimation of parameters of finite populations and introduces the standard sampling designs such as simple random sampling, systematic sampling, probability proportional to size sampling, stratified sampling, cluster and multi-stage sampling. In part II (3 chapters, 121 pp.) estimation through linear modeling is discussed based on ratio and regression methods using information on auxiliary variables. Two phase sampling, domain estimation, variance estimation and model-based optimality of sampling designs as well as analysis of complex survey data are described in part III (5 chapters, 170 pp.).
The final part (4 chapters, 124 pp.) deals with the important practical problems of non-sampling errors, non response, measurement errors and data quality. There are four appendices, one on notations and three exhibiting live data. Each chapter has both theoretical and practical exercises, with answers to selected exercises. There are over 300 references.
As the authors point out, the main objective of this text is “to develop the central ideas in survey sampling from the unified perspective of unequal probability sampling guided by statistical modeling in the derivation of estimators”. In satisfying this, the authors have presented a very clear and lucid material hitherto found in journals and research proceedings. A significant part of the text is devoted to analysis of complex survey data including categorical data tests for finite populations, regression and ratio estimators for domain estimators, synthetic estimation, balanced half-samples, jackknife and bootstrap methods for variance estimation. Following the main theme of the text, the authors have included several non-response and measurement error models.
The book can be used for a one-semester advanced course in survey sampling for which the instructor has to make a careful selection of topics. The authors also suggest some alternatives for this. In summing up, “Model assisted survey sampling” is an important and useful addition.

MSC:
62D05 Sampling theory, sample surveys
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
62-02 Research exposition (monographs, survey articles) pertaining to statistics
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