Robust Nonparametric Regression for Heavy-Tailed Data

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.