On the robustness of the class of stack filters

Abstract

A widely held view in the nonlinear signal processing community is that the class of stack filters is robust. Although this is supported by extensive experimental evidence, no systematic theoretical justification exists, despite the availability of analytical tools for studying robustness of individual stack filters. We focus on rank selection probabilities (RSPs) as measures of robustness as it is well known that other statistical characterizations of stack filters, such as output distributions, breakdown probabilities and output distributional influence functions can be represented in terms of RSPs. We show, in a very general sense, that the class of stack filters is highly robust. It is also shown that almost all stack filters have very similar output distributions for independent and identically distributed (i.i.d.) input signals and, thus, very similar statistical behavior.