##
**Exploring multivariate data with the forward search.**
*(English)*
Zbl 1049.62057

Springer Series in Statistics. New York, NY: Springer (ISBN 0-387-40852-5/hbk). xxiii, 621 p. (2004).

This book deals with procedures to analyze sets of multivariate observations of continuous variables. This is done by a mixture of model fitting and information plots. A basic idea is that of forward search: starting from a small subset of the data, further observations are added and their effects studied.

The procedures consist of three main steps: (1) The search starts with a small, robustly chosen subset of data that excludes outliers. It is used to provide initial parameter estimates. (2) The forward search proceeds, for which a particular way of operating is selected. (3) Monitoring of the statistics is performed during the search. Monitoring is through the analysis of the behavior of the minimum Mahalanobis distance from data not in the subset, as the data are fitted to increasing large subsets, and also through parameter estimates and test statistics.

The procedures are described in general, and then applied to a collection of data sets. The main such sets are 17 in number, ranging from 17 to 341 observations, and from 2 to 28 variables. There are also further sets of data, making a total of 26 sets. They cover a wide range of interesting applications. The data are shown through tables and figures, the latter numbering 390, which means that illustrations are abundant. Reference to multivariate normal distributions is frequent. However, the procedures are given as alternatives to the standard techniques derived from the normal distribution.

The book has two parts. In the first part, chapters 1 to 4, the basic ideas are presented and illustrated in detail. References to computer programs are provided. Chapter 2 surveys the standard statistical theory. Chapter 4 deals with the important topic of transformations.

The second part corresponds to chapters 5 to 8, and covers principal components, discriminant analysis, cluster analysis and spatial linear models. These chapters are organized as follows: starting sections present the techniques known in the literature. Then data sets are processed and the results analyzed and presented to the reader.

Almost all chapters have final sections of references, exercises and their solutions. The book is intended to be a companion to A. Atkinson and M. Riani (the first two authors), Robust regression analysis. (2000; Zbl 0964.62063).

This is an attractive and useful book. It has a wealth of suggestions. Heavy use of computers is done. The results of the analysis are usually presented in graphical form, and as said, the book has 390 graphs.

The procedures consist of three main steps: (1) The search starts with a small, robustly chosen subset of data that excludes outliers. It is used to provide initial parameter estimates. (2) The forward search proceeds, for which a particular way of operating is selected. (3) Monitoring of the statistics is performed during the search. Monitoring is through the analysis of the behavior of the minimum Mahalanobis distance from data not in the subset, as the data are fitted to increasing large subsets, and also through parameter estimates and test statistics.

The procedures are described in general, and then applied to a collection of data sets. The main such sets are 17 in number, ranging from 17 to 341 observations, and from 2 to 28 variables. There are also further sets of data, making a total of 26 sets. They cover a wide range of interesting applications. The data are shown through tables and figures, the latter numbering 390, which means that illustrations are abundant. Reference to multivariate normal distributions is frequent. However, the procedures are given as alternatives to the standard techniques derived from the normal distribution.

The book has two parts. In the first part, chapters 1 to 4, the basic ideas are presented and illustrated in detail. References to computer programs are provided. Chapter 2 surveys the standard statistical theory. Chapter 4 deals with the important topic of transformations.

The second part corresponds to chapters 5 to 8, and covers principal components, discriminant analysis, cluster analysis and spatial linear models. These chapters are organized as follows: starting sections present the techniques known in the literature. Then data sets are processed and the results analyzed and presented to the reader.

Almost all chapters have final sections of references, exercises and their solutions. The book is intended to be a companion to A. Atkinson and M. Riani (the first two authors), Robust regression analysis. (2000; Zbl 0964.62063).

This is an attractive and useful book. It has a wealth of suggestions. Heavy use of computers is done. The results of the analysis are usually presented in graphical form, and as said, the book has 390 graphs.

Reviewer: Raúl Mentz (S. M. de Tucuman)

### MSC:

62Hxx | Multivariate analysis |

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

62A09 | Graphical methods in statistics |