Design of a robust parameter estimator for nominally Laplacian noise

Abstract

In this work we have made use of a geometric approach which quantifies robustness and performance and we finally combine them using a cost function. In particular, we calculate the robustness of the estimate of standard deviation of nominally Laplacian distribution. As this distribution is imperfectly known, we employ a more general family, the generalized Gaussian; Laplacian distribution, is one of the members of this family. We compute parameter estimates and present a classical algorithm which is then analyzed for distribution from the generalized Gaussian family. We calculate the mean squared error according to the censoring height k. We measure performance as a function of (1/MSE) and combine it with robustness using a cost criterion and design a robust estimator which optimizes a mix of performance and robustness specified by the user.