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Robust Kernel Density Estimation by Scaling and Projection in Hilbert Space
Robert A Vandermeulen · Clayton Scott

Mon Dec 08 04:00 PM -- 08:59 PM (PST) @ Level 2, room 210D #None
While robust parameter estimation has been well studied in parametric density estimation, there has been little investigation into robust density estimation in the nonparametric setting. We present a robust version of the popular kernel density estimator (KDE). As with other estimators, a robust version of the KDE is useful since sample contamination is a common issue with datasets. What ``robustness'' means for a nonparametric density estimate is not straightforward and is a topic we explore in this paper. To construct a robust KDE we scale the traditional KDE and project it to its nearest weighted KDE in the $L^2$ norm. Because the squared $L^2$ norm penalizes point-wise errors superlinearly this causes the weighted KDE to allocate more weight to high density regions. We demonstrate the robustness of the SPKDE with numerical experiments and a consistency result which shows that asymptotically the SPKDE recovers the uncontaminated density under sufficient conditions on the contamination.

Author Information

Rob A Vandermeulen (TU Kaiserslautern)
Clay Scott (University of Michigan)

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