Abstract
We propose a robust nonparametric regression method that can deal with heavy-tailed noise and also a heavy-tailed input variable. We decompose the trajectory matrix of the response variable of the regression problem to extract the regression function in a nonparametric way. We implement the decomposition in a robust way using iterative robust linear regressions. We show the effectiveness of the proposed method on synthetic and real data in comparison with two other nonparametric methods and a robust linear method.
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Notes
All of the supplementary materials (MATLAB and R codes) are available at “www.researchgate.net/profile/Ferdos_Gorji/amp.”
We use the method introduced by Chambers et al. (1976) to generate symmetric stable random numbers with \(1<\alpha \le 2\), \(\beta =0\), \(\gamma =1\), and \(\delta =0\).
More explanation about the parameters of heavyPS is available at “http://heavy.mat.utfsm.cl.”
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Acknowledgements
We would like to express our gratitude to the associate editor and two anonymous referees for their practical comments and advice, which helped us to improve our manuscript. We would also like to thank Professor J. P. Nolan for sharing his “Stable” package that we used to estimate the tail index of our real datasets.
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Gorji, F., Aminghafari, M. Robust Nonparametric Regression for Heavy-Tailed Data. JABES 25, 277–291 (2020). https://doi.org/10.1007/s13253-019-00382-2
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DOI: https://doi.org/10.1007/s13253-019-00382-2