Statistical Analysis of Observations of Increasing Dimension

Inbunden, Engelska, 1995

Av V.L. Girko, V. L. Girko

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The limit distribution of the empirical generalized variance, covariance matrices, their eigenvalues and solutions of the system of linear algebraic equations with random coefficients, are an important function of observations in multidimensional statistical analysis. This book is devoted to their investigation. 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 important advantages over 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, control theory of linear stochastic systems, linear stochastic programming, and the theory of experiment planning.

Produktinformation

Utgivningsdatum1995-03-31
Mått160 x 240 x 22 mm
Vikt641 g
FormatInbunden
SpråkEngelska
SerieTheory and Decision Library B
Antal sidor290
Upplaga1995
FörlagKluwer Academic Publishers
ISBN9780792328865

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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.

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.