Format:
1 Online-Ressource (xii, 169 Seiten)
ISBN:
0898712440
,
9780898712445
Series Statement:
CBMS-NSF Regional Conference series in applied mathematics 59
Note:
Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader
,
Includes bibliographical references (s. 153-165)
,
Foreword -- Chapter 1. Background -- Chapter 2. More splines -- Chapter 3. Equivalence and perpendicularity, or, What's so special about splines? -- Chapter 4. Estimating the smoothing parameter -- Chapter 5. "Confidence intervals" -- Chapter 6. Partial spline models -- Chapter 7. Finite-dimensional approximating subspaces -- Chapter 8. Fredholm integral equations of the first kind -- Chapter 9. Further nonlinear generalizations -- Chapter 10. Additive and interaction splines -- Chapter 11. Numerical methods -- Chapter 12. Special topics -- Bibliography
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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
Additional Edition:
Erscheint auch als Druck-Ausgabe, Paperback ISBN 0898712440
Additional Edition:
Erscheint auch als Druck-Ausgabe, Paperback ISBN 9780898712445
Language:
English
Subjects:
Economics
,
Mathematics
Keywords:
Spline
;
Spline
;
Statistik
;
Spline-Approximation
;
Statistik
;
Konferenzschrift
;
Konferenzschrift
DOI:
10.1137/1.9781611970128
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