Spline Models for Observational Data.

Abstract

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.

Keywords

Smoothing splineSpline (mechanical)Applied mathematicsMathematicsPoisson distributionSmoothingContext (archaeology)GaussianMathematical optimizationComputer scienceAlgorithmStatisticsSpline interpolation

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Publication Info

Year: 1991
Type: article
Volume: 86
Issue: 415
Pages: 834-834
Citations: 5024
Access: Closed

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APA Style

                            
                                    Hans‐Georg Müller, 
                                
                                    Grace Wahba
                                
                            (1991). 
                            Spline Models for Observational Data.. 
                            Journal of the American Statistical Association
                            , 86
                            (415)
                            , 834-834.
                            https://doi.org/10.2307/2290434

Identifiers

DOI: 10.2307/2290434