Nonparametric Regression and Generalized Linear Models
A roughness penalty approach
Seiten
1993
Chapman & Hall/CRC (Verlag)
978-0-412-30040-0 (ISBN)
Chapman & Hall/CRC (Verlag)
978-0-412-30040-0 (ISBN)
This study of nonparametric regression and generalized linear models contains chapters on approaches to regression, roughness penalties, extensions of the roughness penalty approach, computing the estimates, interpolating and smoothing splines, one-dimensional case, partial splines, and more.
In recent years, there has been a great deal of interest and activity in the general area of nonparametric smoothing in statistics. This monograph concentrates on the roughness penalty method and shows how this technique provides a unifying approach to a wide range of smoothing problems. The method allows parametric assumptions to be realized in regression problems, in those approached by generalized linear modelling, and in many other contexts.
The emphasis throughout is methodological rather than theoretical, and it concentrates on statistical and computation issues. Real data examples are used to illustrate the various methods and to compare them with standard parametric approaches. Some publicly available software is also discussed. The mathematical treatment is self-contained and depends mainly on simple linear algebra and calculus.
This monograph will be useful both as a reference work for research and applied statisticians and as a text for graduate students and other encountering the material for the first time.
In recent years, there has been a great deal of interest and activity in the general area of nonparametric smoothing in statistics. This monograph concentrates on the roughness penalty method and shows how this technique provides a unifying approach to a wide range of smoothing problems. The method allows parametric assumptions to be realized in regression problems, in those approached by generalized linear modelling, and in many other contexts.
The emphasis throughout is methodological rather than theoretical, and it concentrates on statistical and computation issues. Real data examples are used to illustrate the various methods and to compare them with standard parametric approaches. Some publicly available software is also discussed. The mathematical treatment is self-contained and depends mainly on simple linear algebra and calculus.
This monograph will be useful both as a reference work for research and applied statisticians and as a text for graduate students and other encountering the material for the first time.
P.J. Green, Bristol Univesity. Bernard. W. Silverman St. Peters College, Oxford.
Preface. Introduction. Approaches to Regression. Roughness Penalties. Extensions of the Roughness Penalty Approach. Computing the Estimates. Further Reading. Interpolating and Smoothing Splines. One-Dimensional Case: Further Topics. Partial Splines. Generalized Linear Models. Extending the Model. Thin Plate Splines. Available Software. Reference. Author Index. Subject Index.
| Erscheint lt. Verlag | 1.5.1993 |
|---|---|
| Reihe/Serie | Chapman & Hall/CRC Monographs on Statistics and Applied Probability |
| Sprache | englisch |
| Maße | 152 x 229 mm |
| Gewicht | 500 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| ISBN-10 | 0-412-30040-0 / 0412300400 |
| ISBN-13 | 978-0-412-30040-0 / 9780412300400 |
| Zustand | Neuware |
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