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.