Spline Models for Observational DataSIAM, 1 sept. 1990 - 181 pages 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. Convergence properties, data based smoothing parameter selection, confidence intervals, and numerical methods are established which are appropriate to a number of problems within this framework. Methods for including side conditions and other prior information in solving ill posed inverse problems are provided. 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. |
Table des matières
CB59_ch1 | 1 |
CB59_ch2 | 21 |
CB59_ch3 | 41 |
CB59_ch4 | 45 |
CB59_ch5 | 67 |
CB59_ch6 | 73 |
CB59_ch7 | 95 |
CB59_ch8 | 101 |
CB59_ch9 | 109 |
CB59_ch10 | 127 |
CB59_ch11 | 135 |
CB59_ch12 | 145 |
CB59_backmatter | 153 |
Autres éditions - Tout afficher
Expressions et termes fréquents
algorithm approximation basis functions boundary conditions bounded linear functional computing confidence intervals considered covariance Craven and Wahba cross-validation decomposition defined divided difference eigenfunctions eigenvalues Equations equivalent ET(X example Figure Find ƒ ƒ ² Gaussian Gaussian stochastic process GCV estimate GCV function given H₁ Hilbert space ijth entry interaction splines iteration Kimeldorf and Wahba log tGML Mathematical method minimizer multivariate netlib nonlinear null space numerical Nychka O'Sullivan obtained optimal orthogonal P₁ P₂ penalty functional positive definite positive-definite function properties QR decomposition quadratic quadratic mean R¹(s random variables regression reproducing kernel satisfy Section smoothing parameters smoothing spline solution span spline squared norm Statist stochastic process subspace Suppose t₁ tGcv theorem thin-plate spline total degree less univariate Utreras values variance vector zero ηλ