The Tikhonov method of regularization (MOR) estimator provides a general method for estimation of a nonparametric regression parameter in an abstract linear model with discrete noisy data. An asymptotic analysis is given in which the discrete estimation problem is approximated by a continuous one. Rates of convergence are calculated in a family of norms natural to the problem. The general theory is applied to the estimation of functions from noisy evaluations of the function and one of its derivatives.
Publié le : 1988-06-14
Classification:
41-00,
Nonparametric regression,
method of regularization,
smoothing splines,
rates of convergence,
62G05,
41A25,
47A50
@article{1176350829,
author = {Cox, Dennis D.},
title = {Approximation of Method of Regularization Estimators},
journal = {Ann. Statist.},
volume = {16},
number = {1},
year = {1988},
pages = { 694-712},
language = {en},
url = {http://dml.mathdoc.fr/item/1176350829}
}
Cox, Dennis D. Approximation of Method of Regularization Estimators. Ann. Statist., Tome 16 (1988) no. 1, pp. 694-712. http://gdmltest.u-ga.fr/item/1176350829/