Theoretical foundations of functional data analysis, with an introduction to linear operations
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...
| Otros Autores: | , |
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| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Chichester, England :
Wiley
2015.
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| Edición: | 1st edition |
| Colección: | Wiley series in probability and statistics.
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| Materias: | |
| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009629574006719 |
Tabla de Contenidos:
- 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
- 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
- Chapter 6 Smoothing and regularization6.1 Functional linear model; 6.2 Penalized least squares estimators; 6.3 Bias and variance; 6.4 A computational formula; 6.5 Regularization parameter selection; 6.6 Splines; Chapter 7 Random elements in a Hilbert space; 7.1 Probability measures on a Hilbert space; 7.2 Mean and covariance of a random element of a Hilbert space; 7.3 Mean-square continuous processes and the Karhunen-Lòeve Theorem; 7.4 Mean-square continuous processes in L2(E, B(E),μ); 7.5 RKHS valued processes; 7.6 The closed span of a process; 7.7 Large sample theory
- 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
- 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
