Robust Signal Estimation Based on Influence Function

Abstract

In this paper a class of recursive robust estimators of signal amplitude, based on influence function, is considered. We supposed that signal has a known form and that additive noise is non-Gaussian. As a estimator we used stochastic approximation algorithm with nonlinear transformation of prediction error. Nonlinear transformation determined as a optimization problem with the upper bound on their gross-error sensitivity. The latter is a the supremum of the absolute value of the influence function which is the first derivative of the von Mises's Taylor expansion of statistical functional. Than we proved consistency of estimates using ODE methodology. Also considered asymptotic distribution of estimates. Using Hademard's differentiability of statistical functional we cided set of conditions for asymptotic efficiency of recursive algorithm. Finally we considered estimators which posses the smallest sensitivite possible. Such estimator is the most B-robust and that is median.