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A distribution-free theory of nonpar...

Gy鋌rfi, L榥szl漃.

A distribution-free theory of nonparametric regression

紀錄類型:	書目-電子資源 : 單行本
正題名/作者:	A distribution-free theory of nonparametric regression/ L榥szl漃 Gy鋌rfi [and others].
其他作者:	Gy鋌rfi, L榥szl漃.
出版者:	New York :Springer,�002.
面頁冊數:	1 online resource (xvi, 647 pages) :illustrations.
標題:	Regression analysis. -
電子資源:	Click here for online access to this book (查閱全文) (EBSCO eBook)
ISBN:	0387224424 (electronic bk.)
ISBN:	9780387224428 (electronic bk.)

A distribution-free theory of nonparametric regression
A distribution-free theory of nonparametric regression[electronic resource] /L榥szl漃 Gy鋌rfi [and others]. - New York :Springer,�002. - 1 online resource (xvi, 647 pages) :illustrations. - Springer series in statistics. - Springer series in statistics..

Includes bibliographical references (p. [612]-638) and indexes.

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.

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.

ISBN: 0387224424 (electronic bk.)Subjects--Topical Terms:

153780
Regression analysis.
Index Terms--Genre/Form:

172687
Electronic books.

LC Class. No.: QA278.2 / .D57 2002eb

Dewey Class. No.: 519.5/36

A distribution-free theory of nonparametric regression
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520 $a 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.
588 $a Description based on print version record.
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