Statistical Analysis of Observations of Increasing Dimension

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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.