A general approach for nonparametric fitting of functions and their derivatives with applications to linear circuits identification

The problem of the estimation of functions and their derivatives from noisy observations is discussed. The study is motivated by the interest in nonparametric identification of linear circuits. A general algorithm is proposed and its asymptotic properties are investigated. Three special cases of this algorithm-derived from orthogonal series, the Parzen kernels and the
k_n
nearest neighbor rules-are presented. In the each case the mean square error convergence and the strong convergence is established. The best speed of convergence is found under some assumptions.