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A DistributionFree Theory of Nonparametric Regression (Springer Series in Statistics)by Laszlo Gyorfi
Synopses & ReviewsPublisher Comments:This book provides a systematic indepth 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 distributionfree properties of the estimates. Most consistency results are valid for all distributions of the data. Whenever it is not possible to derive distributionfree 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 distributionfree 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 indepth analysis of nonparametric regression with random design. It covers almost all known estimates. The emphasis is on distributionfree properties of the estimates.
Synopsis:This monograph presents a modern approach to nonparametric regression with random design. 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.
Table of ContentsWhy is Nonparametric Regression Important? * How to Construct Nonparametric Regression Estimates * Lower Bounds * Partitioning Estimates * Kernel Estimates * kNN 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 DataDependent 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
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