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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...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Chichester, West Sussex, United Kingdom :
Wiley,
2015.
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| Temas: | |
| Acceso en línea: | Texto completo (Requiere registro previo con correo institucional) |
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 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.