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Spline Models for Observational Data
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Librairie Eyrolles - Paris 5e
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Spline Models for Observational Data

Spline Models for Observational Data

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

180 pages, parution le 15/03/1990

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

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