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Elliptically Contoured Models in Statistics and Portfolio Theory fully revises the first detailed introduction to the theory of matrix variate elliptically contoured distributions. There are two additional chapters, and all the original chapters of this classic text have been updated. Resources in this book will be valuable for researchers, practitioners, and graduate students in statistics and related fields of finance and engineering. Those interested in multivariate statistical analysis and its application to portfolio theory will find this text immediately useful. In multivariate statistical analysis, elliptical distributions have recently provided an alternative to the normal model. Elliptical distributions have also increased their popularity in finance because of the ability to model heavy tails usually observed in real data. Most of the work, however, is spread out in journals throughout the world and is not easily accessible to the investigators. A noteworthy function of this book is the collection of the most important results on the theory of matrix variate elliptically contoured distributions that were previously only available in the journal-based literature. The content is organized in a unified manner that can serve an a valuable introduction to the subject.
List of contents
Preliminaries.- Basic Properties.- Probability Density Function and Expected Values.- Mixtures of Normal Distributions.- Quadratic Forms and other Functions of Elliptically Contoured Matrices.- Characterization Results.- Estimation.- Hypothesis Testing.- Linear Models.- Skew Elliptically Contoured Distributions.- Application in Portfolio Theory.- Author Index.- Subject Index.
About the author
Arjun Gupta is affiliated with the Department of Statistics at Bowling Green State University. Tamas Varga is a statistical researcher in Hungary. Taras Bodnar is affiliated with the Department of Statistics at Stiftung European University Viadrina.
Summary
Elliptically Contoured Models in Statistics and Portfolio Theory fully revises the first detailed introduction to the theory of matrix variate elliptically contoured distributions. There are two additional chapters, and all the original chapters of this classic text have been updated. Resources in this book will be valuable for researchers, practitioners, and graduate students in statistics and related fields of finance and engineering. Those interested in multivariate statistical analysis and its application to portfolio theory will find this text immediately useful. In multivariate statistical analysis, elliptical distributions have recently provided an alternative to the normal model. Elliptical distributions have also increased their popularity in finance because of the ability to model heavy tails usually observed in real data. Most of the work, however, is spread out in journals throughout the world and is not easily accessible to the investigators. A noteworthy function of this book is the collection of the most important results on the theory of matrix variate elliptically contoured distributions that were previously only available in the journal-based literature. The content is organized in a unified manner that can serve an a valuable introduction to the subject.
Additional text
From the book reviews:
“The book is a thorough presentation of the results from the literature and some new ones and is a product of a careful work of its authors. … the book under review is a useful collection of numerous facts concerning elliptically contoured distributions for random matrices. It may find its place in research libraries as a valuable reference source and will surely appeal to the researches working in the theory of multivariate distributions.” (Ilya S. Molchanov, zbMATH 1306.62028, 2015)
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From the book reviews:
"The book is a thorough presentation of the results from the literature and some new ones and is a product of a careful work of its authors. ... the book under review is a useful collection of numerous facts concerning elliptically contoured distributions for random matrices. It may find its place in research libraries as a valuable reference source and will surely appeal to the researches working in the theory of multivariate distributions." (Ilya S. Molchanov, zbMATH 1306.62028, 2015)
