Jussi Klemelä - Multivariate Nonparametric Regression and Visualization: With R and Applications to Finance

Multivariate Nonparametric Regression and Visualization

WILEY SERIES IN COMPUTATIONAL STATISTICS

Consulting Editors:

Paolo Giudici
University of Pavia, Italy

Geof H. Givens
Colorado State University, USA

Bani K. MallickTexas A&M University, USA

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Klemela Multivariate Nonparametric Regression and Visualization: With R and Applications to Finance

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Library of Congress Cataloging-in-Publication Data:

Klemel, Jussi, 1965
Multivariate nonparametric regression and visualization : with R and applications to finance / Jussi Klemel.
pages cm. (Wiley series in computational statistics ; 699)
Includes bibliographical references and index.
ISBN 978-0-470-38442-8 (hardback)
1. FinanceMathematical models. 2. Visualization. 3. Regression analysis. I. Title.
HG176.5.K55 2014
519.536dc23

2013042095

To my parents

PREFACE

The book is intended for students and researchers who want to learn to apply nonparametric and semiparametric methods and to use visualization tools related to these estimation methods. In particular, the book is intended for students and researchers in quantitative finance who want to apply statistical methods and for students and researchers of statistics who want to learn to apply statistical methods in quantitative finance. The book continues the themes of Klemel (2009), which studied density estimation. The current book focuses on regression function estimation.

The book was written at the University of Oulu, Department of Mathematical Sciences. I wish to acknowledge the support provided by the University of Oulu and the Department of Mathematical Sciences.

The web page of the book is http://cc.oulu.fi/~jklemela/regstruct/ .

JUSSI KLEMEL

Oulu, Finland
October 2013

INTRODUCTION

We study regression analysis and classification, as well as estimation of conditional variances, quantiles, densities, and distribution functions. The focus of the book is on nonparametric methods. Nonparametric methods are flexible and able to adapt to various kinds of data, but they can suffer from the curse of dimensionality and from the lack of interpretability. Semiparametric methods are often able to cope with quite high-dimensional data and they are often easier to interpret, but they are less flexible and their use may lead to modeling errors. In addition to terms nonparametric estimator and semiparametric estimator, we can use the term structured estimator to denote such estimators that arise, for example, in additive models. These estimators obey a structural restriction, whereas the term semiparametric estimator is used for estimators that have a parametric and a nonparametric component.

Nonparametric, semiparametric, and structured methods are well established and widely applied. There are, nevertheless, areas where a further work is useful. We have included three such areas in this book:

One of the main topics of the book are the kernel methods. Kernel methods are easy to implement and computationally feasible, and their definition is intuitive. For example, a kernel regression estimator is a local average of the values of the response variable. Local averaging is a general regression method. In addition to the kernel estimator, examples of local averaging include the nearest-neighbor estimator, the regressogram, and the orthogonal series estimator.

We cover linear regression and generalized linear models. These models can be seen as starting points to many semiparametric and structured regression models. For example, the single index model, the additive model, and the varying coefficient linear regression model can be seen as generalizations of the linear regression model or the generalized linear model.