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 |