V. I. Serdobolskii

Multivariate Statistical Analysis (eBook, PDF)

A High-Dimensional Approach

• Format: PDF

Produktbeschreibung

Multivariate Statistical Analysis

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Produktdetails

• Verlag: Springer Netherlands
• Seitenzahl: 244
• Erscheinungstermin: 9. März 2013
• Englisch
• ISBN-13: 9789401594684
• Artikelnr.: 44063342

Inhaltsangabe

Kolmogorov Asymptotics in Problems of Multivariate Analysis.- Spectral Theory of Large Covariance Matrices.- Approximately Unimprovable Essentially Multivariate Procedures.- 1. Spectral Properties of Large Wishart Matrices.- Wishart Distribution.- Limit Moments of Wishart Matrices.- Limit Formula for the Resolvent of Wishart Matrices.- 2. Resolvents and Spectral Functions of Large Sample Covariance Matrices.- Spectral Functions of Random Gram Matrices.- Spectral Functions of Sample Covariance Matrices.- Limit Spectral Functions of the Increasing Sample Covariance Matrices.- 3. Resolvents and Spectral Functions of Large Pooled Sample Covariance Matrices.- Problem Setting.- Spectral Functions of Pooled Random Gram Matrices.- Spectral Functions of Pooled Sample Covariance Matrices.- Limit Spectral Functions of the Increasing Pooled Sample Covariance Matrices.- 4. Normal Evaluation of Quality Functions.- Measure of Normalizability.- Spectral Functions of Large Covariance Matrices.- Normal Evaluation of Sample Dependent Functionals.- Discussion.- 5. Estimation of High-Dimensional Inverse Covariance Matrices.- Shrinkage Estimators of the Inverse Covariance Matrices.- Generalized Ridge Estimators of the Inverse Covariance Matrices.- Asymptotically Unimprovable Estimators of the Inverse Covariance Matrices.- 6. Epsilon-Dominating Component-Wise Shrinkage Estimators of Normal Mean.- Estimation Function for the Component-Wise Estimators.- Estimators of the Unimprovable Estimation Function.- 7. Improved Estimators of High-Dimensional Expectation Vectors.- Limit Quadratic Risk for a Class of Estimators of Expectation Vectors.- Minimization of the Limit Quadratic Risk.- Statistics to Approximate the Limit Risk Function.- Statistics to Approximate the Extremal limit Solution.- 8. Quadratic Risk of Linear Regression with a Large Number of Random Predictors.- Spectral Functions of Sample Covariance Matrices.- Functionals Depending on the Statistics Sand ?0.- Functionals Depending on Sample Covariance Matrices and Covariance Vectors.- The Leading Part of the Quadratic Risk and its Estimator.- Special Cases.- 9. Linear Discriminant Analysis of Normal Populations with Coinciding Covariance Matrices.- Problem Setting.- Expectation and Variance of Generalized Discriminant Functions.- Limit Probabilities of the Discrimination Errors.- 10. Population Free Quality of Discrimination.- Problem Setting.- Leading Parts of Functionals for Normal Populations.- Leading Parts of Functionals for Arbitrary Populations.- Discussion.- Proofs.- 11. Theory of Discriminant Analysis of the Increasing Number of Independent Variables.- Problem Setting.- A Priori Weighting of Independent Variables.- Minimization of the Limit Error Probability for a Priori Weighting.- Weighting of Independent Variables by Estimators.- Minimization of the Limit Error Probability for Weighting by Estimators.- Statistics to Estimate Probabilities of Errors.- Contribution of Variables to Discrimination.- Selection of a Large Number of Independent Variables.- Conclusions.- References.