Weighted Repeated Median Smoothing and Filtering

We propose weighted repeated median filters and smoothers for robust non-parametric regression in general and for robust signal extraction from time series in particular. The proposed 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. It also allows to improve the efficiency of (unweighted) repeated median filters using larger bandwidths, keeping their properties for distinguishing between outlier sequences and long-term shifts. Robust smoothers based on weighted L1- regression are included for the reason of comparison.