Over the past 15 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 with the aim of showing how it provides a unifying approach to a wide range of smoothing problems. The method allows parametric assumptions to be relaxed both in regression problems and in those approached by generalized linear modelling. The emphasis throughout is methodological rather than theoretical and concentrates on statistical and computational 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 intended to be largely 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 others 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.