Abstract
We propose a method for nonparametric density estimation that exhibits robustness to contamination of the training sample. This method achieves robustness by combining a traditional kernel density estimator (KDE) with ideas from classical M-estimation. We interpret the KDE based on a positive semi-definite kernel as a sample mean in the associated reproducing kernel Hilbert space. Since the sample mean is sensitive to outliers, we estimate it robustly via M-estimation, yielding a robust kernel density estimator (RKDE). An RKDE can be computed efficiently via a kernelized iteratively re-weighted least squares (IRWLS) algorithm. Necessary and sufficient conditions are given for kernelized IRWLS to converge to the global minimizer of the M-estimator objective function. The robustness of the RKDE is demonstrated with a representer theorem, the influence function, and experimental results for density estimation and anomaly detection.
Keywords
MathematicsEstimatorPointwiseMultivariate kernel density estimationKernel density estimationKernel (algebra)Density estimationVariable kernel density estimationApplied mathematicsVariable (mathematics)StatisticsKernel methodMathematical analysisArtificial intelligenceComputer scienceDiscrete mathematicsSupport vector machine
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Publication Info
- Year
- 1992
- Type
- article
- Volume
- 20
- Issue
- 3
- Citations
- 872
- Access
- Closed
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Cite This
George R. Terrell,
David W. Scott
(1992).
Variable Kernel Density Estimation.
The Annals of Statistics
, 20
(3)
.
https://doi.org/10.1214/aos/1176348768
Identifiers
- DOI
- 10.1214/aos/1176348768