Madan Lal Puri

Takesi Hayakawa

Kameo Matsushita

The Third Pacific Area Statistical Conference was held under the auspices of the Pacific Statistical Institute and with the support and cooperation of the Foundation for Advancement of International Science, the Japan Statistical Society and the Institute of Statistical Mathematics. The main theme of the conference was ''Statistical Sciences and Data Analysis''. The purpose was to bring together researchers in statistics and related fields to exchange results and problems in topics of mutual interest. The papers in this volume have been presented at the conference and have been carefully refereed and edited before their inclusion in the proceedings.

Proceedings of the Third Pacific Area Statistical Conference

Statistical Sciences and Data Analysis

Arak M. Mathai

Serge B. Provost

The book deals with bilinear forms in real random vectors and their generalizations as well as zonal polynomials and their applications in handling generalized quadratic and bilinear forms. The book is mostly self-contained. It starts from basic principles and brings the readers to the current research level in these areas. It is developed with detailed proofs and illustrative examples for easy readability and self-study. Several exercises are proposed at the end of the chapters. The complicated topic of zonal polynomials is explained in detail in this book. The book concentrates on the theoretical developments in all the topics covered. Some applications are pointed out but no detailed application to any particular field is attempted. This book can be used as a textbook for a one-semester graduate course on quadratic and bilinear forms and/or on zonal polynomials. It is hoped that this book will be a valuable reference source for graduate students and research workers in the areas of mathematical statistics, quadratic and bilinear forms and their generalizations, zonal polynomials, invariant polynomials and related topics, and will benefit statisticians, mathematicians and other theoretical and applied scientists who use any of the above topics in their areas. Chapter 1 gives the preliminaries needed in later chapters, including some Jacobians of matrix transformations. Chapter 2 is devoted to bilinear forms in Gaussian real ran dom vectors, their properties, and techniques specially developed to deal with bilinear forms where the standard methods for handling quadratic forms become complicated.

Takesi Hayakawa

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