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.
Provides a systematic in-depth analysis of nonparametric regression
with random design. Covers almost all known estimates such as classical
local and averaging estimates including kernel.