Spline models for observational data: Based on a series of 10 lectures at Ohio State University at Columbus, Mar. 23-27, 1987
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia, Pa.
Society for Industrial and Applied Mathematics
1990
|
| Schriftenreihe: | CBMS-NSF Regional Conference series in applied mathematics
59 |
| Schlagworte: | |
| Online-Zugang: | TUM01 UBW01 UBY01 UER01 Volltext |
| Beschreibung: | 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 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 |
| Beschreibung: | 1 Online-Ressource (xii, 169 Seiten) |
| ISBN: | 0898712440 9780898712445 |
| DOI: | 10.1137/1.9781611970128 |
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| 245 | 1 | 0 | |a Spline models for observational data |b Based on a series of 10 lectures at Ohio State University at Columbus, Mar. 23-27, 1987 |c Grace Wahba |
| 264 | 1 | |a Philadelphia, Pa. |b Society for Industrial and Applied Mathematics |c 1990 | |
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| 490 | 1 | |a CBMS-NSF Regional Conference series in applied mathematics |v 59 | |
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| 500 | |a Includes bibliographical references (s. 153-165) | ||
| 500 | |a 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 | ||
| 500 | |a 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 | ||
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Datensatz im Suchindex
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| spelling | Wahba, Grace Verfasser aut Spline models for observational data Based on a series of 10 lectures at Ohio State University at Columbus, Mar. 23-27, 1987 Grace Wahba Philadelphia, Pa. Society for Industrial and Applied Mathematics 1990 1 Online-Ressource (xii, 169 Seiten) txt rdacontent c rdamedia cr rdacarrier CBMS-NSF Regional Conference series in applied mathematics 59 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 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 Spline theory Mathematical statistics Statistik (DE-588)4056995-0 gnd rswk-swf Spline-Approximation (DE-588)4182394-1 gnd rswk-swf Spline (DE-588)4182391-6 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift 1987 Columbus Ohio gnd-content 2\p (DE-588)1071861417 Konferenzschrift gnd-content Spline (DE-588)4182391-6 s DE-604 Statistik (DE-588)4056995-0 s Spline-Approximation (DE-588)4182394-1 s Erscheint auch als Druck-Ausgabe, Paperback 0898712440 Erscheint auch als Druck-Ausgabe, Paperback 9780898712445 CBMS-NSF Regional Conference series in applied mathematics 59 (DE-604)BV046682627 59 https://doi.org/10.1137/1.9781611970128 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Wahba, Grace Spline models for observational data Based on a series of 10 lectures at Ohio State University at Columbus, Mar. 23-27, 1987 CBMS-NSF Regional Conference series in applied mathematics Spline theory Mathematical statistics Statistik (DE-588)4056995-0 gnd Spline-Approximation (DE-588)4182394-1 gnd Spline (DE-588)4182391-6 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4182394-1 (DE-588)4182391-6 (DE-588)1071861417 |
| title | Spline models for observational data Based on a series of 10 lectures at Ohio State University at Columbus, Mar. 23-27, 1987 |
| title_auth | Spline models for observational data Based on a series of 10 lectures at Ohio State University at Columbus, Mar. 23-27, 1987 |
| title_exact_search | Spline models for observational data Based on a series of 10 lectures at Ohio State University at Columbus, Mar. 23-27, 1987 |
| title_full | Spline models for observational data Based on a series of 10 lectures at Ohio State University at Columbus, Mar. 23-27, 1987 Grace Wahba |
| title_fullStr | Spline models for observational data Based on a series of 10 lectures at Ohio State University at Columbus, Mar. 23-27, 1987 Grace Wahba |
| title_full_unstemmed | Spline models for observational data Based on a series of 10 lectures at Ohio State University at Columbus, Mar. 23-27, 1987 Grace Wahba |
| title_short | Spline models for observational data |
| title_sort | spline models for observational data based on a series of 10 lectures at ohio state university at columbus mar 23 27 1987 |
| title_sub | Based on a series of 10 lectures at Ohio State University at Columbus, Mar. 23-27, 1987 |
| topic | Spline theory Mathematical statistics Statistik (DE-588)4056995-0 gnd Spline-Approximation (DE-588)4182394-1 gnd Spline (DE-588)4182391-6 gnd |
| topic_facet | Spline theory Mathematical statistics Statistik Spline-Approximation Spline Konferenzschrift 1987 Columbus Ohio Konferenzschrift |
| url | https://doi.org/10.1137/1.9781611970128 |
| volume_link | (DE-604)BV046682627 |
| work_keys_str_mv | AT wahbagrace splinemodelsforobservationaldatabasedonaseriesof10lecturesatohiostateuniversityatcolumbusmar23271987 |