A Distribution-Free Theory of Nonparametric Regression

Laszlo Györfi, Michael Kohler, Adam Krzyzak, Harro Walk

662 pages, parution le 21/10/2002

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Résumé

This book provides a systematic in-depth analysis of nonparametric regression with random design. It covers almost all known estimates such as classical local averaging estimates including kernel, partitioning and nearest neighbor estimates, least squares estimates using splines, neural networks and radial basis function networks, penalized least squares estimates, local polynomial kernel estimates, and orthogonal series estimates. The emphasis is on distribution-free properties of the estimates. Most consistency results are valid for all distributions of the data. Whenever it is not possible to derive distribution-free results, as in the case of the rates of convergence, the emphasis is on results which require as few constrains on distributions as possible, on distribution-free inequalities, and on adaptation.
The relevant mathematical theory is systematically developed and requires only a basic knowledge of probability theory. The book will be a valuable reference for anyone interested in nonparametric regression and is a rich source of many useful mathematical techniques widely scattered in the literature. In particular, the book introduces the reader to empirical process theory, martingales and approximation properties of neural networks.

Contents

Why is Nonparametric Regression Important?
How to Construct Nonparametric Regression Estimates
Lower Bounds
Partitioning Estimates
Kernel Estimates
k-NN Estimates
Splitting the Sample
Cross Validation
Uniform Laws of Large Numbers
Least Squares Estimates I: Consistency
Least Squares Estimates II: Rate of Convergence
Least Squares Estimates III: Complexity Regularization
Consistency of Data-Dependent Partitioning Estimates
Univariate Least Squares Spline Estimates
Multivariate Least Squares Spline Estimates
Neural Networks Estimates
Radial Basis Function Networks
Orthogonal Series Estimates
Advanced Techniques from Empirical Process Theory
Penalized Least Squares Estimates I: Consistency
Penalized Least Squares Estimates II: Rate of Convergence
Dimension Reduction Techniques
Strong Consistency of Local Averaging Estimates
Semi-Recursive Estimates
Recursive Estimates
Censored Observations
Dependent Observations.

L'auteur - Laszlo Györfi

Györfi, László, Budapest University of Technology and Economics, Hungary, Budapest

L'auteur - Michael Kohler

Kohler, Michael, University of Stuttgart, Germany;

L'auteur - Adam Krzyzak

Krzyzak, Adam, Concordia University, Montreal, ON, Canada;

L'auteur - Harro Walk

Walk, Harro, University of Stuttgart, Germany

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Laszlo Györfi, Michael Kohler, Adam Krzyzak, Harro Walk
Parution	21/10/2002
Nb. de pages	662
Format	16 x 24
Couverture	Broché
Poids	1055g
Intérieur	Noir et Blanc
EAN13	9780387954417
ISBN13	978-0-387-95441-7