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Estimating a regression function. (English) Zbl 0709.62040

A general regression problem is considered. The unknown regression function is proposed to lie in a possible nonparametric class of functions G. The author considered the methods of least squares, of least absolute deviations and of penalized least squares. These procedures differ in respect to their loss functions, but the author provides a general technique to obtain rates of convergence for the resulting estimators. The link with empirical process theory makes it possible to relate the rates of convergence to the entropy of G.
Reviewer: S.Zwanzig

MSC:

62G07 Density estimation
62J02 General nonlinear regression
60G50 Sums of independent random variables; random walks
60B10 Convergence of probability measures
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