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- W4295116590 abstract "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. This yields a scaled and projected KDE (SPKDE). 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." @default.
- W4295116590 created "2022-09-10" @default.
- W4295116590 creator A5024149142 @default.
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- W4295116590 date "2014-11-17" @default.
- W4295116590 modified "2023-09-26" @default.
- W4295116590 title "Robust Kernel Density Estimation by Scaling and Projection in Hilbert Space" @default.
- W4295116590 doi "https://doi.org/10.48550/arxiv.1411.4378" @default.
- W4295116590 hasPublicationYear "2014" @default.
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