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Complex surveys. Analysis of categorical data. (English) Zbl 1394.62004

Singapore: Springer (ISBN 978-981-10-0870-2/hbk; 978-981-10-0871-9/ebook). xv, 248 p. (2016).
The reason behind writing this book, according to the author, is to review “some of the ideas that have blown out in the field of analysis of categorical data from complex surveys”. It is nice to have such a collection spread over in the literature at one place and it is what the author tried to do in this book. He arranged these ideas systematically in eight chapters with illustrative examples.
Chapter 1 (26 pp.) introduces preliminaries related to basic sampling designs and briefly touches upon the design-based and model-based methods of inference in sampling from finite populations. A plan of the book can be found in the last section. Chapter 2 (40 pp.) discusses ‘design effects’ and ‘misspecification effects’ as well as non-parametric variance estimation. In the third chapter (30 pp.), classical models in categorical data analysis such as log-linear model, logistic regression model are reviewed. Chapters 4 (37 pp.), 5 (22 pp.), 6 (21 pp.) and 7 (16 pp.) describe the techniques of analysis of categorical data under a full model, under log-linear models, under logistic regression model and when misclassification errors are present respectively. The final Chapter 8 (28 pp.) details some procedures for obtaining approximate maximum likelihood and related estimators from survey data. There is an appendix on asymptotic properties of multinomial distribution in 7 subsections. There are just over 200 references at the end of the book. The book will be useful to researchers in the field of analysis of complex survey data dealing with several categories. A survey practitioner would perhaps look for some numerical examples and computer outputs which probably is not the aim of this ‘research monograph’. A quick look showed a few misprints such as ‘Hartly’ on p. 1, reference to Hansen et al. (1953) with ‘Hurwitz’ missing (p. 14), Basu D. (with an extra K (p. 241)), ‘Hanurav’ (p. 243: paper appeared in the name of Hanumantha Rao, T. V. , who later changed his name), Sinha B. K. (p. 247) ‘Un’ sampling….

MSC:

62-02 Research exposition (monographs, survey articles) pertaining to statistics
62D05 Sampling theory, sample surveys
62G07 Density estimation
62J12 Generalized linear models (logistic models)
62E20 Asymptotic distribution theory in statistics
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