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Abstract Nonlinear data smoothers provide a practical method of finding smooth traces for data confounded with possibly long-tailed or occasionally spikey noise. They are resistant to the effects of extreme observations that are not part of the local pattern, yet they are able to respond rapidly to well-supported patterns. This article defines a collection of nonlinear smoothers based upon running medians and presents methods for describing and comparing their performance. The characterizations of the smoothers presented here reveal some with excellent low-pass transfer characteristics, negligible Gibbs rebound, and resistance to the effects of non-Gaussian disturbances.
Paul F. Velleman (Mon,) studied this question.