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Nonparametric L1 regression for spherical data with heavy-tailed dependent errors

This talk considers the nonlinear regression model whose predictor is a random vector on a hyper-sphere. This setting has various applications such as seismic wave analysis, analysis for orientation of wild fire, etc. It is well known that the classical method in “linear statistic” does not work for spherical random vectors. To construct a robust estimator for the nonlinear regression function, this talk employees L1-regression method and kernel-type objective function. The proposed local-linear estimator has asymptotic normality regardless of whether the innovation process has infinite variance or dependence structure. Some simulation experiments illustrate desired finite sample properties of the proposed method. (Joint work with Holger Dette (Ruhr-Universität Bochum))