Conference Proceedings

Outlier detection and robust estimation in nonparametric regression

D Kong, H Bondell, W Shen

Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics | Published : 2018

Abstract

This paper studies outlier detection and robust estimation for nonparametric regression problems. We propose to include a subject-specific mean shift parameter for each data point such that a nonzero parameter will identify its corresponding data point as an outlier. We adopt a regularization approach by imposing a roughness penalty on the regression function and a shrinkage penalty on the mean shift parameter. An efficient algorithm has been proposed to solve the double penalized regression problem. We discuss a data-driven simultaneous choice of two regularization parameters based on a combination of generalized cross validation and modified Bayesian information criterion. We show that t..

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