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Spline-Modelle für Beobachtungsdaten von Grace Wahba (1990, Trade Paperback)-
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eBay-Artikelnr.:226741462154
Artikelmerkmale
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- Country/Region of Manufacture
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- ISBN
- 9780898712445
Über dieses Produkt
Product Identifiers
Publisher
Society for Industrial AND Applied Mathematics
ISBN-10
0898712440
ISBN-13
9780898712445
eBay Product ID (ePID)
1099928
Product Key Features
Number of Pages
182 Pages
Language
English
Publication Name
Spline Models for Observational Data
Subject
Probability & Statistics / General, Mathematical Analysis
Publication Year
1990
Type
Textbook
Subject Area
Mathematics
Series
Cbms-Nsf Regional Conference Series in Applied Mathematics Ser.
Format
Trade Paperback
Dimensions
Item Height
0.4 in
Item Weight
12 Oz
Item Length
9.7 in
Item Width
6.7 in
Additional Product Features
Intended Audience
Scholarly & Professional
LCCN
89-028687
Dewey Edition
20
Reviews
'The book provides a rather complete unified treatment of smoothing splines, starting with the classical polynomial smoothing spline, and including the periodic smoothing spline on a circle, both scalar and vector-valued splines on the sphere, and thin plate splines in the plane and in higher dimensional Euclidean spaces. In addition, it treats two special kinds of smoothing splines called partial splines and additive splines. The splines discussed here have numerous practical applications in data fitting of economical, medical, meteorological, and radiation data. She provides applications to the solution of Fredholm integral equations of the first kind, fluid flow problems in porous media, and certain inverse problems.' Larry L. Schumaker, Vanderbilt University, SIAM Review, 'This is a thorough account of non-parametric regression using splines, eschewing other approaches, and approaching splines themselves via the technology of reproducing kernel Hilbert spaces. The result is an impressively unified, consistent, treatment of a wide variety of problems, some really quite hard ... This is an impressive record of research, offering stimulation for further investigation.'P. J. Green, Short Book Reviews of the International Statistical Institute, 'This is a thorough account of non-parametric regression using splines, eschewing other approaches, and approaching splines themselves via the technology of reproducing kernel Hilbert spaces. The result is an impressively unified, consistent, treatment of a wide variety of problems, some really quite hard … This is an impressive record of research, offering stimulation for further investigation.' P. J. Green, Short Book Reviews of the International Statistical Institute, ‘The book provides a rather complete unified treatment of smoothing splines, starting with the classical polynomial smoothing spline, and including the periodic smoothing spline on a circle, both scalar and vector-valued splines on the sphere, and thin plate splines in the plane and in higher dimensional Euclidean spaces. In addition, it treats two special kinds of smoothing splines called partial splines and additive splines. The splines discussed here have numerous practical applications in data fitting of economical, medical, meteorological, and radiation data. She provides applications to the solution of Fredholm integral equations of the first kind, fluid flow problems in porous media, and certain inverse problems.’Larry L. Schumaker, Vanderbilt University, SIAM Review, 'The book provides a rather complete unified treatment of smoothing splines, starting with the classical polynomial smoothing spline, and including the periodic smoothing spline on a circle, both scalar and vector-valued splines on the sphere, and thin plate splines in the plane and in higher dimensional Euclidean spaces. In addition, it treats two special kinds of smoothing splines called partial splines and additive splines. The splines discussed here have numerous practical applications in data fitting of economical, medical, meteorological, and radiation data. She provides applications to the solution of Fredholm integral equations of the first kind, fluid flow problems in porous media, and certain inverse problems.' Larry L. Schumaker, Vanderbilt University, , SIAM Review, ' ... The reviewer considers the monograph a valuable contribution and recommends it strongly to everyone with some interest in this important area of statistics.' Girdhar G. Agarwal, Mathematical Reviews, ' … The reviewer considers the monograph a valuable contribution and recommends it strongly to everyone with some interest in this important area of statistics.' Girdhar G. Agarwal, Mathematical Reviews, ' ... The reviewer considers the monograph a valuable contribution and recommends it strongly to everyone with some interest in this important area of statistics.'Girdhar G. Agarwal, Mathematical Reviews, ‘ … The reviewer considers the monograph a valuable contribution and recommends it strongly to everyone with some interest in this important area of statistics.’Girdhar G. Agarwal, Mathematical Reviews, 'This is a thorough account of non-parametric regression using splines, eschewing other approaches, and approaching splines themselves via the technology of reproducing kernel Hilbert spaces. The result is an impressively unified, consistent, treatment of a wide variety of problems, some really quite hard ... This is an impressive record of research, offering stimulation for further investigation.' P. J. Green, Short Book Reviews of the International Statistical Institute, 'The book provides a rather complete unified treatment of smoothing splines, starting with the classical polynomial smoothing spline, and including the periodic smoothing spline on a circle, both scalar and vector-valued splines on the sphere, and thin plate splines in the plane and in higher dimensional Euclidean spaces. In addition, it treats two special kinds of smoothing splines called partial splines and additive splines. The splines discussed here have numerous practical applications in data fitting of economical, medical, meteorological, and radiation data. She provides applications to the solution of Fredholm integral equations of the first kind, fluid flow problems in porous media, and certain inverse problems.'Larry L. Schumaker, Vanderbilt University, SIAM Review, ‘This is a thorough account of non-parametric regression using splines, eschewing other approaches, and approaching splines themselves via the technology of reproducing kernel Hilbert spaces. The result is an impressively unified, consistent, treatment of a wide variety of problems, some really quite hard … This is an impressive record of research, offering stimulation for further investigation.’P. J. Green, Short Book Reviews of the International Statistical Institute
Series Volume Number
No. 59
Illustrated
Yes
Dewey Decimal
519.5
Table Of Content
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 Author Index.
Synopsis
Peovides an introduction into the more theoretical aspects of the use of spline models. This book develops a theory and practice for the estimation of functions from noisy data on functionals., 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.
LC Classification Number
QA224.W34 1990
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