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Theoretical foundations of functional data analysis, with an introduction to linear operators /

Provides essential coverage of functional data analysis and related areas. This book provides a uniquely broad compendium of the key mathematical concepts and results that are relevant for the theoretical development of functional data analysis (FDA). The self-contained treatment of selected topics...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Hsing, Tailen, 1955-
Otros Autores: Eubank, Randall L., 1952-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Chichester, West Sussex, United Kingdom : Wiley, 2015.
Temas:
Acceso en línea:Texto completo (Requiere registro previo con correo institucional)

MARC

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100 1 |a Hsing, Tailen,  |d 1955- 
245 1 0 |a Theoretical foundations of functional data analysis, with an introduction to linear operators /  |c Tailen Hsing, Randall Eubank. 
264 1 |a Chichester, West Sussex, United Kingdom :  |b Wiley,  |c 2015. 
264 4 |c ©2015 
300 |a 1 online resource 
336 |a text  |b txt  |2 rdacontent 
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338 |a online resource  |b cr  |2 rdacarrier 
504 |a Includes bibliographical references and index. 
588 0 |a Print version record and CIP data provided by publisher. 
505 0 |a Cover; Contents; Preface; Chapter 1 Introduction; 1.1 Multivariate analysis in a nutshell; 1.2 The path that lies ahead; Chapter 2 Vector and function spaces; 2.1 Metric spaces; 2.2 Vector and normed spaces; 2.3 Banach and Lp spaces; 2.4 Inner Product and Hilbert spaces; 2.5 The projection theorem and orthogonal decomposition; 2.6 Vector integrals; 2.7 Reproducing kernel Hilbert spaces; 2.8 Sobolev spaces; Chapter 3 Linear operator and functionals; 3.1 Operators; 3.2 Linear functionals; 3.3 Adjoint operator; 3.4 Nonnegative, square-root, and projection operators; 3.5 Operator inverses. 
505 8 |a 3.6 Fréchet and Gâteaux derivatives3.7 Generalized Gram-Schmidt decompositions; Chapter 4 Compact operators and singular value decomposition; 4.1 Compact operators; 4.2 Eigenvalues of compact operators; 4.3 The singular value decomposition; 4.4 Hilbert-Schmidt operators; 4.5 Trace class operators; 4.6 Integral operators and Mercer's Theorem; 4.7 Operators on an RKHS; 4.8 Simultaneous diagonalization of two nonnegative definite operators; Chapter 5 Perturbation theory; 5.1 Perturbation of self-adjoint compact operators; 5.2 Perturbation of general compact operators. 
505 8 |a Chapter 8 Mean and covariance estimation8.1 Sample mean and covariance operator; 8.2 Local linear estimation; 8.3 Penalized least-squares estimation; Chapter 9 Principal components analysis; 9.1 Estimation via the sample covariance operator; 9.2 Estimation via local linear smoothing; 9.3 Estimation via penalized least squares; Chapter 10 Canonical correlation analysis; 10.1 CCA for random elements of a Hilbert space; 10.2 Estimation; 10.3 Prediction and regression; 10.4 Factor analysis; 10.5 MANOVA and discriminant analysis; 10.6 Orthogonal subspaces and partial cca; Chapter 11 Regression. 
505 8 |a 11.1 A functional regression model11.2 Asymptotic theory; 11.3 Minimax optimality; 11.4 Discretely sampled data; References; Index; Notation Index; Wiley Series in Probability and Statistics; EULA. 
520 |a Provides essential coverage of functional data analysis and related areas. This book provides a uniquely broad compendium of the key mathematical concepts and results that are relevant for the theoretical development of functional data analysis (FDA). The self-contained treatment of selected topics of functional analysis and operator theory includes reproducing kernel Hilbert spaces, singular value decomposition of compact operators on Hilbert spaces and perturbation theory for both self-adjoint and non self-adjoint operators. The probabilistic foundation for FDA is described from the perspecti. 
590 |a O'Reilly  |b O'Reilly Online Learning: Academic/Public Library Edition 
650 0 |a Multivariate analysis. 
650 0 |a Statistical functionals. 
650 0 |a Linear operators. 
650 6 |a Analyse multivariée. 
650 6 |a Fonctionnelles statistiques. 
650 6 |a Opérateurs linéaires. 
650 7 |a MATHEMATICS  |x Mathematical Analysis.  |2 bisacsh 
650 7 |a MATHEMATICS  |x Calculus.  |2 bisacsh 
650 7 |a Linear operators.  |2 fast  |0 (OCoLC)fst00999087 
650 7 |a Multivariate analysis.  |2 fast  |0 (OCoLC)fst01029105 
650 7 |a Statistical functionals.  |2 fast  |0 (OCoLC)fst01132062 
700 1 |a Eubank, Randall L.,  |d 1952- 
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