Theory and Decision Library B

Statistical Analysis of Observations of Increasing Dimension

Authors: Girko, V.L.

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About this book

Statistical Analysis of Observations of Increasing Dimension is devoted to the investigation of the limit distribution of the empirical generalized variance, covariance matrices, their eigenvalues and solutions of the system of linear algebraic equations with random coefficients, which are an important function of observations in multidimensional statistical analysis. A general statistical analysis is developed in which observed random vectors may not have density and their components have an arbitrary dependence structure. The methods of this theory have very important advantages in comparison with existing methods of statistical processing. The results have applications in nuclear and statistical physics, multivariate statistical analysis in the theory of the stability of solutions of stochastic differential equations, in control theory of linear stochastic systems, in linear stochastic programming, in the theory of experiment planning.

About the authors

Vyacheslav L. Girko is Professor of Mathematics in the Department of Applied Statistics at the National University of Kiev and the University of Kiev Mohyla Academy. He is also affiliated with the Institute of Mathematics, Ukrainian Academy of Sciences. His research interests include multivariate statistical analysis, discriminant analysis, experiment planning, identification and control of complex systems, statistical methods in physics, noise filtration, matrix analysis, and stochastic optimization. He has published widely in the areas of multidimensional statistical analysis and theory of random matrices.

Table of contents (6 chapters)

  • Introduction to General Statistical Analysis

    Girko, Vyacheslav L.

    Pages 1-31

  • Limit Theorems for the Empirical Generalized Variance

    Girko, Vyacheslav L.

    Pages 32-57

  • The Canonical Equations C 1, ... , C 3 for the Empirical Covariance Matrix

    Girko, Vyacheslav L.

    Pages 58-121

  • Limit Theorems for the Eigenvalues of Empirical Covariance Matrices

    Girko, Vyacheslav L.

    Pages 122-170

  • G 2-estimator for the Stieltjes Transform of the Normalized Spectral Function of Covariance Matrices

    Girko, Vyacheslav L.

    Pages 171-212

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-94-015-8567-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $199.00
price for USA
  • ISBN 978-0-7923-2886-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $199.00
price for USA
  • ISBN 978-90-481-4413-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Statistical Analysis of Observations of Increasing Dimension
Authors
Series Title
Theory and Decision Library B
Series Volume
28
Copyright
1995
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-94-015-8567-5
DOI
10.1007/978-94-015-8567-5
Hardcover ISBN
978-0-7923-2886-5
Softcover ISBN
978-90-481-4413-6
Edition Number
1
Number of Pages
XXI, 290
Topics