Introduction to variance estimation.

*(English)*Zbl 0581.62009
Springer Series in Statistics. New York etc.: Springer-Verlag. XI, 427 p. DM 160.00 (1985).

This book may be thought of as a handbook of classical variance estimation methods. The author has summarized a lot of knowledge on random groups methods, balanced half-samples and jackknife method and their use to estimate the variance of several usual population parameters.

Explanation of the methods mentioned above is divided into three main chapters of the book (2 to 4). In the preface one may learn that bootstrap technique has been omitted on purpose and that the author does not discuss variance estimation neither from the prediction-theory nor from the Bayesian viewpoint. The conventional character of treatment is stressed, superpopulation models are not employed for the main tasks.

Chapters 5 and 6 deal with slightly different problems - the use of generalized variance functions and Taylor series for indirect variance estimation. Brief explanation of the underlying theory is supplemented by instructive real-data examples, which is the case in the preceding chapters, too.

Another problem again is treated in chapter 7 - variance estimation for systematic sampling. The author not only shows some useful methods for this popular sampling strategy, but also warns about lack of theoretical background in some situations.

The character of a handbook is underlined in the last chapter that summarizes main problems of field variance estimation, and in appendices (except of the rather theoretial Appendix B) which contain much information useful for survey statisticians - Hadamard matrices, often- used transformations and examples of computer software. In Appendix D the author deals in short with the effect of measurement errors on variance estimation, taking into account the simplest possible model of independent \(N(0,\sigma^ 2_ i)\) errors.

The explanations in the book are straightforward and easy-to-read even for those with only elementary education in sampling. On the other hand, relatively simple sampling strategies are treated and the extension to more complex surveys will not be so easy for this class of readers.

Explanation of the methods mentioned above is divided into three main chapters of the book (2 to 4). In the preface one may learn that bootstrap technique has been omitted on purpose and that the author does not discuss variance estimation neither from the prediction-theory nor from the Bayesian viewpoint. The conventional character of treatment is stressed, superpopulation models are not employed for the main tasks.

Chapters 5 and 6 deal with slightly different problems - the use of generalized variance functions and Taylor series for indirect variance estimation. Brief explanation of the underlying theory is supplemented by instructive real-data examples, which is the case in the preceding chapters, too.

Another problem again is treated in chapter 7 - variance estimation for systematic sampling. The author not only shows some useful methods for this popular sampling strategy, but also warns about lack of theoretical background in some situations.

The character of a handbook is underlined in the last chapter that summarizes main problems of field variance estimation, and in appendices (except of the rather theoretial Appendix B) which contain much information useful for survey statisticians - Hadamard matrices, often- used transformations and examples of computer software. In Appendix D the author deals in short with the effect of measurement errors on variance estimation, taking into account the simplest possible model of independent \(N(0,\sigma^ 2_ i)\) errors.

The explanations in the book are straightforward and easy-to-read even for those with only elementary education in sampling. On the other hand, relatively simple sampling strategies are treated and the extension to more complex surveys will not be so easy for this class of readers.

Reviewer: J.Herzmann

##### MSC:

62D05 | Sampling theory, sample surveys |

62-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics |