Distribution-Free Theory of Nonparametric Regression

Name: Distribution-Free Theory of Nonparametric Regression
Price: 259.67 USD
Availability: InStock
ISBN: 9780387954417

ISBN-10: 0387954414

ISBN-13: 9780387954417

Edition: 2002

Authors: Lï¿½szlï¿½ Gyï¿½rfi, Michael Kï¿½hler, Adam Krzyzak, Harro Walk

List price: $229.00

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Description:

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…

Book details

List price: $229.00
Copyright year: 2002
Publisher: Springer
Publication date: 8/12/2002
Binding: Hardcover
Pages: 650
Size: 6.25" wide x 9.25" long x 1.50" tall
Weight: 2.332
Language: English



Preface



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



Semirecursive Estimates



Recursive Estimates



Censored Observations



Dependent Observations


App. A: Tools


Notation


Bibliography


Author Index


Subject Index