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About this book
In the last few decades the accumulation of large amounts of in formation in numerous applications. has stimtllated an increased in terest in multivariate analysis. Computer technologies allow one to use multi-dimensional and multi-parametric models successfully. At the same time, an interest arose in statistical analysis with a de ficiency of sample data. Nevertheless, it is difficult to describe the recent state of affairs in applied multivariate methods as satisfactory. Unimprovable (dominating) statistical procedures are still unknown except for a few specific cases. The simplest problem of estimat ing the mean vector with minimum quadratic risk is unsolved, even for normal distributions. Commonly used standard linear multivari ate procedures based on the inversion of sample covariance matrices can lead to unstable results or provide no solution in dependence of data. Programs included in standard statistical packages cannot process 'multi-collinear data' and there are no theoretical recommen dations except to ignore a part of the data. The probability of data degeneration increases with the dimension n, and for n > N, where N is the sample size, the sample covariance matrix has no inverse. Thus nearly all conventional linear methods of multivariate statis tics prove to be unreliable or even not applicable to high-dimensional data.
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Table of contents (13 chapters)
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Front Matter
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Back Matter
Authors and Affiliations
Bibliographic Information
Book Title: Multivariate Statistical Analysis
Book Subtitle: A High-Dimensional Approach
Authors: V. Serdobolskii
Series Title: Theory and Decision Library B
DOI: https://doi.org/10.1007/978-94-015-9468-4
Publisher: Springer Dordrecht
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media B.V. 2000
Hardcover ISBN: 978-0-7923-6643-0Published: 31 October 2000
Softcover ISBN: 978-90-481-5593-4Published: 09 December 2010
eBook ISBN: 978-94-015-9468-4Published: 09 March 2013
Edition Number: 1
Number of Pages: XII, 244
Topics: Statistics, general, Quality Control, Reliability, Safety and Risk, Econometrics, Artificial Intelligence, Statistics for Life Sciences, Medicine, Health Sciences