Multivariate Statistical Analysis
Subtitle: A High-Dimensional Approach
By: by V. Serdobolskii
Series: Theory and Decision Library, Series B: Mathematical and Statistical Methods -- 41; Theory and Decision Library, Series B: Mathematical and Statistical Methods -- 41
Publisher: Springer Netherlands
Published: 2000
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] :
Number of pages: 244
ISBN-13: 9789048155934; 9789401594684
Subjects: System safety; Statistics; Econometrics; Artificial intelligence
Description: This book presents a new branch of mathematical statistics aimed at constructing unimprovable methods of multivariate analysis, multi-parametric estimation, and discriminant and regression analysis. In contrast to the traditional consistent Fisher method of statistics, the essentially multivariate technique is based on the decision function approach by A. Wald. Developing this new method for high dimensions, comparable in magnitude with sample size, provides stable approximately unimprovable procedures in some wide classes, depending on an arbitrary function. A remarkable fact is established: for high-dimensional problems, under some weak restrictions on the variable dependence, the standard quality functions of regularized multivariate procedures prove to be independent of distributions. For the first time in the history of statistics, this opens the possibility to construct unimprovable procedures free from distributions. Audience: This work will be of interest to researchers and graduate students whose work involves statistics and probability, reliability and risk analysis, econometrics, machine learning, medical statistics, and various applications of multivariate analysis.
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