A Distribution-Free Theory of Nonparametric Regression

• Main Authors: Györfi, László (Author), Kohler, Michael (Author), Krzyżak, Adam (Author), Walk, Harro (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2002.
• Series: Springer Series in Statistics,
• Subjects: Statistics.; Statistical Theory and Methods.

The regression estimation problem has a long history. Already in 1632 Galileo Galilei used a procedure which can be interpreted as ?tting a linear relationship to contaminated observed data. Such ?tting of a line through a cloud of points is the classical linear regression problem. A solution of thi...

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
• Semirecursive Estimates
• Recursive Estimates
• Censored Observations
• Dependent Observations.