Cross-validation in nonparametric regression with outliers

By D. Leung. 2005

105 citations recorded by the source corpus.

A popular data-driven method for choosing the bandwidth in standard kernel regression is cross-validation. Even when there are outliers in the data, robust kernel regression can be used to estimate the unknown regression curve [Robust and Nonlinear Time Series Analysis. Lecture Notes in Statist. (1984) 26 163-184]. However, under these circumstances standard cross-validation is no longer a satisfactory bandwidth selector because it is unduly influenced by extreme prediction errors caused by the existence of these outliers. A more robust method proposed here is a cross-validation method that discounts the extreme prediction errors. In large samples the robust method chooses consistent bandwidths, and the consistency of the method is practically independent of the form in which extreme prediction errors are discounted. Additionally, evaluation of the method's finite sample behavior in a simulation demonstrates that the proposed method performs favorably. This method can also he applied to other problems, for example, model selection, that require cross-validation.

Subfields: Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/da70ef9593246153ff06817ae4e3f9afe39768cb

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In Control and Systems Engineering

In Statistics and Probability

Citations in the corpus

Autoreject: Automated artifact rejection for MEG and EEG data (2016, methodology): “The idea of using the median in the context of cross-validation has been previously proposed in the statistics literature in order to deal also with outliers (Leung, 2005; De Brabanter et al., 2003).”
A survey of Bayesian predictive methods for model assessment, selection and comparison (2012, background): “Choice of a particular utility function can also amplify the effect of rare observations in the proxy sample, as demonstrated in a non-Bayesian cross-validation setting by Leung (2005).”
A fast and efficient implementation of qualitatively constrained quantile smoothing splines (2007, background): “See Härdle (1990), Hastie and Tibshirani (1990), Green and Silverman (1994), Wang and Scott (1994), He and Ng (1999), Mammen et al. (2001), Oh et al. (2004), and Leung (2005) for additional references.”