A Distribution-Free Theory of Nonparametric Regression

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.

Inhalt

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