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Spline Models for Observational Data

Spline Models for Observational Data

Part of CBMS-NSF Regional Conference Series in Applied Mathematics

  • Date Published: September 1990
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Paperback
  • isbn: 9780898712445


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About the Authors
  • 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.

    • Introduces the more theoretical uses of spline models
    • Covers estimation of functions from noisy data on functionals
    • Methods for including side conditions and other prior information in solving ill-posed inverse problems are covered
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    Reviews & endorsements

    '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, 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

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    Product details

    • Date Published: September 1990
    • format: Paperback
    • isbn: 9780898712445
    • length: 180 pages
    • dimensions: 257 x 170 x 11 mm
    • weight: 0.321kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    1. Background
    2. More splines
    3. Equivalence and perpendicularity, or, what's so special about splines?
    4. Estimating the smoothing parameter
    5. 'Confidence intervals'
    6. Partial spline models
    7. Finite dimensional approximating subspaces
    8. Fredholm integral equations of the first kind
    9. Further nonlinear generalizations
    10. Additive and interaction splines
    11. Numerical methods
    12. Special topics
    Author index.

  • Author

    Grace Wahba, University of Wisconsin, Madison

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