Statistical Analysis of Observations of Increasing Dimension

1995
ISBN: 978-0-7923-2886-5
Verlag: Springer Netherlands

Buch, Englisch, Band 28, 290 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1370 g

Reihe: Theory and Decision Library B

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.

Zielgruppe

Research

Autoren/Hrsg.

Girko, V. L.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung

Inhaltsverzeichnis

1. Introduction to General Statistical Analysis.- 2. Limit Theorems for the Empirical Generalized Variance.- 3. The Canonical Equations C1,.,C3 for the Empirical Covariance Matrix.- 4. Limit Theorems for the Eigenvalues of Empirical Covariance Matrices.- 5. G2-estimator for the Stieltjes Transform of the Normalized Spectral Function of Covariance Matrices.- 6. Statistical Estimators for Solutions of Systems of Linear Algebraic Equations.- References.

Über Autor(innen)

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.