Spline Models for Observational Data (CBMS-NSF Regional Conference Series in Applied Mathematics, Series Number 59) - Softcover

Wahba, Grace

Softcover

ISBN 10: 0898712440 ISBN 13: 9780898712445

Publisher: SIAM: Society for Industrial and Applied Mathematics, 1990

Synopsis

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.

About this title

Book Description

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.

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

'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

Edition details

• Publisher: SIAM: Society for Industrial and Applied Mathematics
• Publication date: 1990
• Language: English
• ISBN 10: 0898712440
• ISBN 13: 9780898712445
• Binding: Paperback
• Number of pages: 180