Spline models for observational data Based on a series of 10 lectures at Ohio State University at Columbus, Mar. 23-27, 1987
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Philadelphia, Pa.
Society for Industrial and Applied Mathematics
1990
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| Schriftenreihe: | CBMS-NSF Regional Conference series in applied mathematics
59 |
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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 | |
| 300 | |a 1 Online-Ressource (xii, 169 Seiten) | ||
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| 490 | 1 | |a CBMS-NSF Regional Conference series in applied mathematics |v 59 | |
| 500 | |a Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader | ||
| 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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| 650 | 4 | |a Mathematical statistics | |
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Datensatz im Suchindex
| DE-BY-TUM_katkey | 1805803 |
|---|---|
| DE-BY-TUM_local_url | Verlag https://doi.org/10.1137/1.9781611970128 |
| _version_ | 1816713696233127936 |
| any_adam_object | |
| author | Wahba, Grace |
| author_facet | Wahba, Grace |
| author_role | aut |
| author_sort | Wahba, Grace |
| author_variant | g w gw |
| building | Verbundindex |
| bvnumber | BV039747288 |
| classification_rvk | QH 233 SI 196 SK 830 |
| collection | ZDB-72-SIA |
| ctrlnum | (OCoLC)873886423 (DE-599)BVBBV039747288 |
| discipline | Mathematik Wirtschaftswissenschaften |
| doi_str_mv | 10.1137/1.9781611970128 |
| format | Electronic eBook |
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| id | DE-604.BV039747288 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-25T17:37:10Z |
| institution | BVB |
| isbn | 0898712440 9780898712445 |
| language | English |
| lccn | 89028687 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024594819 |
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| physical | 1 Online-Ressource (xii, 169 Seiten) |
| psigel | ZDB-72-SIA |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | marc |
| series | CBMS-NSF Regional Conference series in applied mathematics |
| series2 | CBMS-NSF Regional Conference series in applied mathematics |
| 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 |