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A Distribution-Free Theory of Nonparametric Regression

Librairie Eyrolles - Paris 5e
Indisponible

A Distribution-Free Theory of Nonparametric Regression

A Distribution-Free Theory of Nonparametric Regression

Laszlo Györfi, Michael Kohler, Adam Krzyzak, Harro Walk

662 pages, parution le 21/10/2002

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

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