[share_ebook] Spline Models for Observational Data (CBMS-NSF Regional Conference Series in Applied Mathematics)


Author: Grace Wahba

Date: 1990-09-30

Pages: 180

Publisher: SIAM: Society for Industrial and Applied Mathematics

Category: Study

Tag: Mathematics


Posted on 2011-11-29, by sharebookfree.

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Spline Models for Observational Data (CBMS-NSF Regional Conference Series in Applied Mathematics)


Spline Models for Observational Data (CBMS-NSF Regional Conference Series in Applied Mathematics)
Grace Wahba | SIAM: Society for Industrial and Applied Mathematics | 1990-09-30 | 180 pages | English | PDF

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.


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