Multivariate observations.

*(English)*Zbl 0627.62052
Wiley Series in Probability and Mathematical Statistics. Probability and Mathematical Statistics. New York etc.: John Wiley & Sons. XX, 686 p. (TUB, Fachbibl. Stat.: 85 291) (1984).

The basic prerequisites for reading this book are a good knowledge of matrix algebra and an acquaintance with the multivariate normal distribution, multiple linear regression, and simple analysis of variance and covariance models. This book could be regarded as a companion volume to the author’s book ‘Linear regression analysis.’ (1977; Zbl 0354.62055).

Chapter 1 discusses the nature of multivariate data and problems of simultaneous inference. Chapter 2 selects from the extensive subject of multivariate distribution theory sufficient ideas to indicate the breadth of the subject and to provide a basis for later proofs. Attention is focused on the multivariate normal distribution, Wishart’s distribution, Hotelling’s \(T^ 2\) distribution, together with the multivariate beta distribution and some of its derivatives. Inference for the multivariate normal, both in the one- and two-sample cases, is discussed extensively in Chapter 3, while Chapter 4 surveys graphical and data-oriented techniques. Chapter 5 discusses at length the many practical methods for expressing multivariate data in fewer dimensions in the hope of tracking down clustering or internal structure more effectively.

The growing field of discriminant analysis is reviewed in Chapter 6, while Chapter 7 endeavors to summarize the essentials of the almost unmanageable body of literature on cluster analysis. Chapters 8 and 9 develop linear models, with the general theory given in Chapter 8 and applications to simple multivariate analysis of variance and covariance models given in Chapter 9. The final chapter, Chapter 10, is mainly concerned with computational techniques; however, log-linear models and incomplete data are also discussed briefly.

Appendices A and B summarize a number of useful results in matrix algebra, with projection matrices discussed in Appendix B. Order statistics and probability plotting are considered in Appendix C, and Appendix D is a collection of useful statistical tables. Finally, there is a set of outline solutions for the exercises.

Chapter 1 discusses the nature of multivariate data and problems of simultaneous inference. Chapter 2 selects from the extensive subject of multivariate distribution theory sufficient ideas to indicate the breadth of the subject and to provide a basis for later proofs. Attention is focused on the multivariate normal distribution, Wishart’s distribution, Hotelling’s \(T^ 2\) distribution, together with the multivariate beta distribution and some of its derivatives. Inference for the multivariate normal, both in the one- and two-sample cases, is discussed extensively in Chapter 3, while Chapter 4 surveys graphical and data-oriented techniques. Chapter 5 discusses at length the many practical methods for expressing multivariate data in fewer dimensions in the hope of tracking down clustering or internal structure more effectively.

The growing field of discriminant analysis is reviewed in Chapter 6, while Chapter 7 endeavors to summarize the essentials of the almost unmanageable body of literature on cluster analysis. Chapters 8 and 9 develop linear models, with the general theory given in Chapter 8 and applications to simple multivariate analysis of variance and covariance models given in Chapter 9. The final chapter, Chapter 10, is mainly concerned with computational techniques; however, log-linear models and incomplete data are also discussed briefly.

Appendices A and B summarize a number of useful results in matrix algebra, with projection matrices discussed in Appendix B. Order statistics and probability plotting are considered in Appendix C, and Appendix D is a collection of useful statistical tables. Finally, there is a set of outline solutions for the exercises.

##### MSC:

62Hxx | Multivariate analysis |

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

62-07 | Data analysis (statistics) (MSC2010) |

62J10 | Analysis of variance and covariance (ANOVA) |