Linear models and generalizations. Least squares and alternatives. With contributions by Michael Schomaker. 3rd extended ed.

*(English)*Zbl 1151.62063
Springer Series in Statistics. Berlin: Springer (ISBN 978-3-540-74226-5/hbk). xix, 570 p. (2008).

The book gives an up-to-date and comprehensive account of the theory and applications of linear models along with a number of new results. Throughout its ten chapters as well as its appendices, it covers theoretical issues and practical applications that make it suitable and useful not only to students but also to researchers and consultants in statistics.

More specifically, the first chapter of the book provides an introduction to linear models and regression analysis that constitutes the subject matter of the book. Chapter 2 describes the simple linear regression models and standard statistical approaches, such as direct regression, inverse regression, orthogonal regression, etc., in order to lay the foundations for better understanding of the topics of the next chapters. Chapter 3 presents standard procedures for estimation and testing in multiple linear regression models, while chapter 4 addresses issues related to generalised linear regression models. Chapter 5 is devoted to estimation under exact or stochastic linear restrictions, while chapter 6 presents the theory of optimal linear prediction along with recent related studies. Sensitivity analysis and analysis of incomplete data sets are the topics discussed in chapters 7 and 8, respectively, while chapter 9 contains recent contributions to robust statistical inference. Chapter 10, finally, describes model extensions for categorical responses and explanatory variables.

The book includes also three appendices presenting standard theorems and proofs of matrix algebra, a few statistical tables, and an overview of available software for regression models.

More specifically, the first chapter of the book provides an introduction to linear models and regression analysis that constitutes the subject matter of the book. Chapter 2 describes the simple linear regression models and standard statistical approaches, such as direct regression, inverse regression, orthogonal regression, etc., in order to lay the foundations for better understanding of the topics of the next chapters. Chapter 3 presents standard procedures for estimation and testing in multiple linear regression models, while chapter 4 addresses issues related to generalised linear regression models. Chapter 5 is devoted to estimation under exact or stochastic linear restrictions, while chapter 6 presents the theory of optimal linear prediction along with recent related studies. Sensitivity analysis and analysis of incomplete data sets are the topics discussed in chapters 7 and 8, respectively, while chapter 9 contains recent contributions to robust statistical inference. Chapter 10, finally, describes model extensions for categorical responses and explanatory variables.

The book includes also three appendices presenting standard theorems and proofs of matrix algebra, a few statistical tables, and an overview of available software for regression models.

Reviewer: Vangelis Grigoroudis (Chania)

##### MSC:

62J05 | Linear regression; mixed models |

62J12 | Generalized linear models (logistic models) |

62-02 | Research exposition (monographs, survey articles) pertaining to statistics |

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

62F35 | Robustness and adaptive procedures (parametric inference) |

62F30 | Parametric inference under constraints |