Ebook: Statistical Analysis of Observations of Increasing Dimension

Statistical Analysis of Observations of IncreasingDimension 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.

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Statistical Analysis of Observations of IncreasingDimension 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.

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Statistical Analysis of Observations of IncreasingDimension 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.

Content:
Front Matter....Pages i-xxi
Introduction to General Statistical Analysis....Pages 1-31
Limit Theorems for the Empirical Generalized Variance....Pages 32-57
The Canonical Equations C 1, ... , C 3 for the Empirical Covariance Matrix....Pages 58-121
Limit Theorems for the Eigenvalues of Empirical Covariance Matrices....Pages 122-170
G 2-estimator for the Stieltjes Transform of the Normalized Spectral Function of Covariance Matrices....Pages 171-212
Statistical Estimators for Solutions of Systems of Linear Algebraic Equations....Pages 213-277
Back Matter....Pages 278-290

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Statistical Analysis of Observations of IncreasingDimension 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.

Content:
Front Matter....Pages i-xxi
Introduction to General Statistical Analysis....Pages 1-31
Limit Theorems for the Empirical Generalized Variance....Pages 32-57
The Canonical Equations C 1, ... , C 3 for the Empirical Covariance Matrix....Pages 58-121
Limit Theorems for the Eigenvalues of Empirical Covariance Matrices....Pages 122-170
G 2-estimator for the Stieltjes Transform of the Normalized Spectral Function of Covariance Matrices....Pages 171-212
Statistical Estimators for Solutions of Systems of Linear Algebraic Equations....Pages 213-277
Back Matter....Pages 278-290
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