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| MULTIPARAMETRIC STATISTICS
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By
Vadim Serdobolskii, Moscow State Institute of Electronics and Mathematics, Russia
Description
This monograph presents mathematical theory of statistical models described by the essentially large number of unknown parameters, comparable
with sample size but can also be much larger. In this meaning, the proposed theory can be called "essentially multiparametric". It is
developed on the basis of the Kolmogorov asymptotic approach in which sample size increases along with the number of unknown parameters.
This theory opens a way for solution of central problems of multivariate statistics, which up until now have not been solved. Traditional
statistical methods based on the idea of an infinite sampling often break down in the solution of real problems, and, dependent on data,
can be inefficient, unstable and even not applicable. In this situation, practical statisticians are forced to use various heuristic
methods in the hope the will find a satisfactory solution.
Mathematical theory developed in this book presents a regular technique
for implementing new, more efficient versions of statistical procedures. Near exact solutions are constructed for a number of concrete
multi-dimensional problems: estimation of expectation vectors, regression and discriminant analysis, and for the solution to large systems
of empiric linear algebraic equations. It is remarkable that these solutions prove to be not only non-degenerating and always stable,
but also near exact within a wide class of populations.
In the conventional situation of small dimension and large sample size these
new solutions far surpass the classical, commonly used consistent ones. It can be expected in the near future, for the most part, traditional
multivariate statistical software will be replaced by the always reliable and more efficient versions of statistical procedures implemented
by the technology described in this book.
This monograph will be of interest to a variety of specialists working with the theory of
statistical methods and its applications. Mathematicians would find new classes of urgent problems to be solved in their own regions.
Specialists in applied statistics creating statistical packages will be interested in more efficient methods proposed in the book.
Advantages of these methods are obvious: the user is liberated from the permanent uncertainty of possible instability and inefficiency
and gets algorithms with unimprovable accuracy and guaranteed for a wide class of distributions.
A large community of specialists applying
statistical methods to real data will find a number of always stable highly accurate versions of algorithms that will help them to better
solve their scientific or economic problems. Students and postgraduates will be interested in this book as it will help them get at the
foremost frontier of modern statistical science.
Audience
Specialists in mathematical statistics and applied statistics, statistical software engineers, students specializing in mathematical and applied statistics, researchers, and economists
Contents
Foreword
Preface
Chapter 1. Introduction: The Development of Multiparametric Statistics
Chapter 2. Fundamental Problem of Statistics
Chapter 3. Spectral Theory of Large Sample Covariance Matrices
Chapter 4. Asymptitically Unimprovable Solution of Multivariate Problems
Chapter 5. Multiparametric Discriminant Analysis
Chapter 6. Theory of Solution to High-Order Systems of Empirical Linear Algebraic
Equations
Appendix
References
Index
| Bibliographic details |
Hardbound, 334 pages, publication date: SEP-2007
ISBN-13: 978-0-444-53049-3
ISBN-10: 0-444-53049-5
Imprint: ELSEVIER
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| Price and Ordering |
Price:
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EUR 73.95
GBP 63
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Last update: 5 Sep 2009
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