Introduction to Nonparametric Regression aims at exactly what the title says: an introduction to the subject. This is achieved by giving the basic concepts a simple and lucid presentation. Starting from the parametric approach, we now consider a regression problem with no a priori knowledge about the form of the true function which is to be estimated.
Takezawa starts at the very beginning by explaining the problem and the need for nonparametric regression. This is done very nicely with lots of examples and intuitive explanations. This method of presentation is sustained throughout the book. Chapter 2 covers smoothing techniques, including a detailed exposition of the hat matrix and smoothing splines. One-dimensional regression and multidimensional smoothing are covered in great detail. Briefly, the author covers some aspects of pattern recognition. This chapter would be of great interest to practitioners (for example in the finance industry).
This book is packed with examples. One can really see the attention the author has given to his presentation the subject. Graphical presentation strictly follows theoretical concepts. A hidden little gem of the book is the S-Plus code presented at the end of each chapter. The code clearly explains how certain graphics or examples were constructed. S-Plus code is quite detailed and easy to follow. Furthermore, each chapter contains designated problems. There are quite a few of them, ranging from data analysis using S-Plus to proof type problems.
This book is very suitable for self study, as the presentation is very lucid and easy to follow. S-Plus code and numerous graphical figures should provide adequate help. Good knowledge of linear algebra and statistics should be sufficient as background. Since nonparametric regression is a very applied subject, the book is suitable primarily for graduate students and professionals, as well as for researchers. Given the style of presentation this book will highly be appreciated by students.
Ita Cirovic Donev is a PhD candidate at the University of Zagreb. She hold a Masters degree in statistics from Rice University. Her main research areas are in mathematical finance; more precisely, statistical mehods of credit and market risk. Apart from the academic work she does consulting work for financial institutions.