Statistical Analysis of Observations of Increasing Dimension

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 import...

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Bibliographic Details
Main Author: Girko, V.L.
Format: eBook
Language:English
Published: Dordrecht Springer Netherlands 1995, 1995
Edition:1st ed. 1995
Series:Theory and Decision Library B, Mathematical and Statistical Methods
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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245 0 0 |a Statistical Analysis of Observations of Increasing Dimension  |h Elektronische Ressource  |c by V.L. Girko 
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505 0 |a 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 
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653 |a Probability Theory 
653 |a Linear Algebra 
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653 |a Probabilities 
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520 |a 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