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V.L. Girko
This book contains the results of 30 years of investigation by theauthor into the creation of a new theory on statistical analysis ofobservations, based on the principle of random arrays of randomvectors and matrices of increasing dimensions. It describes limitphenomena of sequences of random observations, which occupy a centralplace in the theory of random matrices. This is the first book toexplore statistical analysis of random arrays and provides thenecessary tools for such analysis. This book is a naturalgeneralization of multidimensional statistical analysis and aims toprovide its readers with new, improved estimators of this analysis.
The book consists of 14 chapters and opens with the theory of samplerandom matrices of fixed dimension, which allows to envelop not onlythe problems of multidimensional statistical analysis, but also someimportant problems of mechanics, physics and economics. The secondchapter deals with all 50 known canonical equations of the newstatistical analysis, which form the basis for finding new andimproved statistical estimators. Chapters 3-5 contain detailedproof of the three main laws on the theory of sample random matrices.In chapters 6-10 detailed, strong proofs of the Circular andElliptic Laws and their generalization are given. In chapters 11-13the convergence rates of spectral functions are given for thepractical application of new estimators and important questions onrandom matrix physics are considered. The final chapter contains 54new statistical estimators, which generalize the main estimators ofstatistical analysis.
This book will be of value and interest to a variety of readers:students, engineers, applied mathematicians, statisticians, andeconomists, who want to understand how a new representation ofobservations, namely random arrays, helps to solve problems. Theresults obtained in this book define a new area in statistics:statistical analysis of random arrays.
1998; xxiv+674 pages
ISBN 90-6764-293-2
Price (all prices are subject to change without notice): EUR 352/US$ 503
VSPPostal address: P.O. Box 9000, 2300 PA Leiden, The Netherlands