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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.

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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