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Approximation of method of regularization estimators. (English) Zbl 0671.62044
Summary: The Tikhonov method of regularization (MOR) estimator provides a general method for estimation of a non-parametric 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.

MSC:
62G05 Nonparametric estimation
47A99 General theory of linear operators
41A25 Rate of convergence, degree of approximation
47A50 Equations and inequalities involving linear operators, with vector unknowns
47A10 Spectrum, resolvent
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