Weighted Repeated Median Smoothing and Filtering

We propose weighted repeated median filters and smoothers for robust nonparametric regression in general and for robust online signal extraction from time series in particular. The new methods allow us 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 nonlinearities 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 examined for comparison.

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