Weighted repeated median smoothing and filtering

• 成果类型: Article
• 署名作者: Fried, Roland; Einbeck, Jochen; Gather, Ursula
• 署名单位: Dortmund University of Technology; Durham University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214507000001166
• 发表日期: 2007
• 页码: 1300-1308
• 关键词: signal extraction; regression; breakdown; estimators

摘要

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 I regression, are examined for comparison.