Buch, Englisch, 244 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 400 g
A High-Dimensional Approach
Buch, Englisch, 244 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 400 g
Reihe: Theory and Decision Library B
ISBN: 978-90-481-5593-4
Verlag: Springer
Multivariate Statistical Analysis
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Technische Wissenschaften Technik Allgemein Technische Zuverlässigkeit, Sicherheitstechnik
- Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie
- Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
- Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung
- Medizin | Veterinärmedizin Medizin | Public Health | Pharmazie | Zahnmedizin Medizin, Gesundheitswesen Medizinische Mathematik & Informatik
- Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Wissensbasierte Systeme, Expertensysteme
- Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
- Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
- Technische Wissenschaften Maschinenbau | Werkstoffkunde Produktionstechnik Industrielle Qualitätskontrolle
- Technische Wissenschaften Elektronik | Nachrichtentechnik Elektronik Robotik
Weitere Infos & Material
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.
