Multidimensional Statistical Analysis and Theory of Random Matrices (eBook)

Frontmatter -- PREFACE -- Welcoming remarks -- Principal Procedures for Statistical Analysis of Random Arrays (SARA) -- CONTENTS -- Some remarks and a bibliography on the Kantorovich inequality -- Band random matrices and quantum chaos -- Weighted continuous metric scaling -- Canonical equation for the resolvent of empirical covariance matrices pencil -- Strong Law for the eigenvalues of empirical covariance matrices -- On the asymptotic behavior of Markov chains with small random perturbations of transition probabilities -- Multivariate statistical inference involving circulant matrices: A review -- Asymptotics of eigenvalue-normed eigenvectors of sample variance and correlation matrices -- Formal density expansions via multivariate mixtures -- Double shrinkage estimators of ratio of variances -- On sequential search for significant variables of unknown function -- Heirarchical random matrices and operators. Application to Anderson model -- Asymptotic properties of invariant tests -- New classes of probability inequalities for some classical distributions -- Equivariant estimation of a subspace -- Optimal design of experiments for multivariate response in two-factor linear models -- Multivariate analysis: Does it really work in statistical applications? -- Robust estimation and testing the mean vector -- Detection of outliers in the presence of multicollinearity -- Estimation in multivariate elliptically contoured linear models II -- Mean and covariance structure analysis with missing data -- Multivariate elliptically contoured linear models and some aspects of the theory of random matrices