Elliptically Contoured Models in Statistics and Portfolio Theory - Gupta, Arjun K.; Varga, Tamas; Bodnar, Taras; SpringerLink (Online service) (New York, NY : Springer New York : Imprint: Springer, 2013)
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.
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.
Keywords: Statistics; Mathematical statistics; Economics -- Statistics; Statistics; Statistical Theory and Methods; Statistics for Business/Economics/Mathematical Finance/Insurance.