Spline Models for Observational Data

Grace Wahba - Collection Cbms-NSF Regional Conference Series in A

180 pages, parution le 15/03/1990

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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

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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