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This is a revised new edition to the classic volume that presents the first detailed introduction to the theory of matrix variate elliptically contoured distributions. In the revised version, all chapters will be completely updated and two chapters are added: Chapter 10 entitled Skew Elliptically Contoured Distributions and Chapter 11 entitled Application in Portfolio Theory . The text shows how even a simple form of the skewness in the asset returns can dramatically influence the performance of the test on the structure of the global minimum variance portfolio. The obtained results can be applied in the small sample case as well. In the empirical study, the authors apply their results to real data of several stocks included in the Dow Jones index. This book will continue to be a valuable resource for researchers and graduate students in statistics and related fields of finance and engineering whose interests involve multivariate statistical analysis.