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This title in other editions

A Distribution-Free Theory of Nonparametric Regression (Springer Series in Statistics)

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Synopses & Reviews

Publisher Comments:

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.

Synopsis:

 This book provides a systematic in-depth analysis of nonparametric regression with random design. It covers almost all known estimates. The emphasis is on distribution-free properties of the estimates.

Table of 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

Product Details

ISBN:
9781441929983
Author:
Gyorfi, Laszlo
Publisher:
Springer
Author:
Walk, Harro
Author:
Kohler, Michael
Author:
Krzyzak, Adam
Location:
New York, NY
Subject:
Statistics
Subject:
Statistical Theory and Methods
Subject:
Mathematics | Probability and Statistics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Subject:
Mathematical statistics
Copyright:
Edition Description:
Softcover reprint of hardcover 1st ed. 2002
Series:
Springer Series in Statistics
Publication Date:
20101201
Binding:
TRADE PAPER
Language:
English
Pages:
664
Dimensions:
235 x 155 mm 2030 gr

Related Subjects


Science and Mathematics » Botany » General
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Statistics

A Distribution-Free Theory of Nonparametric Regression (Springer Series in Statistics) New Trade Paper
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Product details 664 pages Not Avail - English 9781441929983 Reviews:
"Synopsis" by ,  This book provides a systematic in-depth analysis of nonparametric regression with random design. It covers almost all known estimates. The emphasis is on distribution-free properties of the estimates.
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