
Spline Models for Observational Data
Grace Wahba - Collection Cbms-NSF Regional Conference Series in A
Résumé
This book serves well as an introduction into the more theoretical aspects of the use of spline models. It develops a theory and practice for the estimation of functions from noisy data on functionals. The simplest example is the estimation of a smooth curve, given noisy observations on a finite number of its values. The estimate is a polynomial smoothing spline. By placing this smoothing problem in the setting of reproducing kernel Hilbert spaces, a theory is developed which includes univariate smoothing splines, thin plate splines in d dimensions, splines on the sphere, additive splines, and interaction splines in a single framework. A straightforward generalization allows the theory to encompass the very important area of (Tikhonov) regularization methods for ill-posed inverse problems.
Convergence properties, data based smoothing parameter selection, confidence intervals, and numerical methods are established which are appropriate to a wide variety of problems which fall within this framework. Methods for including side conditions and other prior information in solving ill-posed inverse problems are included. Data which involves samples of random variables with Gaussian, Poisson, binomial, and other distributions are treated in a unified optimization context. Experimental design questions, i.e., which functionals should be observed, are studied in a general context. Extensions to distributed parameter system identification problems are made by considering implicitly defined functionals.
Sommaire
- Background
- More splines
- Equivalence and perpendicularity, or, what's so special about splines?
- Estimating the smoothing parameter
- 'Confidence intervals'
- Partial spline models
- Finite dimensional approximating subspaces
- Fredholm integral equations of the first kind
- Further nonlinear generalizations
- Additive and interaction splines
- Numerical methods
- Special topics; Bibliography; Author index
Caractéristiques techniques
PAPIER | |
Éditeur(s) | SIAM: Society for Industrial and Applied Mathematics |
Auteur(s) | Grace Wahba |
Collection | Cbms-NSF Regional Conference Series in A |
Parution | 15/03/1990 |
Nb. de pages | 180 |
Couverture | Relié |
Poids | 321g |
Intérieur | Noir et Blanc |
EAN13 | 9780898712445 |
ISBN13 | 978-0-8987-1244-5 |
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