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Weighted Repeated Median Smoothing and Filtering

Fried, Roland; Einbeck, Jochen; Gather, Ursula

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Authors

Roland Fried

Ursula Gather



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.

Citation

Fried, R., Einbeck, J., & Gather, U. (2007). Weighted Repeated Median Smoothing and Filtering. Journal of the American Statistical Association, 102(480), 1300-1308. https://doi.org/10.1198/016214507000001166

Journal Article Type Article
Online Publication Date Oct 1, 2007
Publication Date 2007-12
Deposit Date Jun 20, 2008
Publicly Available Date Jun 20, 2008
Journal Journal of the American Statistical Association
Print ISSN 0162-1459
Electronic ISSN 1537-274X
Publisher Taylor and Francis Group
Peer Reviewed Peer Reviewed
Volume 102
Issue 480
Pages 1300-1308
DOI https://doi.org/10.1198/016214507000001166
Keywords Signal extraction, Robust regression, Outliers, Breakdown point.

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