Kernel Smoothing

Preface

Typically, patterns in real data, which we may call curves or surfaces, will not follow simple rules. However, there may be a sufficiently good description in terms of a finite number of interpretable parameters. When this is not the case, or if the parametric description is too complex, a nonparametric approach is an option. In developing nonparametric curve estimation methods, however, sometimes we may take advantage of the vast array of available parametric statistical methods and adapt these to the nonparametric setting. While assessing properties of the nonparametric curve estimators, we will use asymptotic arguments.

This book grew out of a set of lecture notes for a course on smoothing given to the graduate students of Seminar für Statistik (Department of Mathematics, ETH, Zürich). To understand the material presented here, knowledge of linear algebra, calculus, and a background in statistical inference, in particular the theory of estimation, testing, and linear models should suffice. The textbooks Statistical Inference (Chapman & Hall) by Samuel David Silvey, Regression Analysis, Theory, Methods and Applications (Springer-Verlag) by Ashis Sen and Muni Srivastava, Linear Statistical Inference, second edition (John Wiley) by Calyampudi Radhakrishna Rao, and Robert Serfling’s book Approximation Theorems of Mathematical Statistics (John Wiley) are excellent sources for background material. For nonparametric curve estimation, there are several good books and in ...