Weighted repeated median smoothing and filtering.

Abstract

We propose weighted repeated median filters and smoothers for robust non-parametric regression in general and for robust online signal extraction from time series in particular. The new methods allow to remove outlying sequences and to preserve discontinuities (shifts) in the underlying regression function (the signal) in the presence of local linear trends. Suitable weighting of the observations according to their distances in the design space reduces the bias arising from non-linearities and improves the efficiency using larger bandwidths, while still distinguishing long-term shifts from outlier sequences. Other localized robust regression techniques like S-, M- and MM-estimators as well as weighted L_1-regression are included for comparison.