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Title: Robust functional quantile regression Authors:  Ufuk Beyaztas - Marmara University (Turkey) [presenting]
Mujgan Tez - Marmara University (Turkey)
Han Lin Shang - Macquarie University (Australia)
Abstract: Scalar-on-function quantile regression is a powerful regression model to characterize the entire conditional distribution of a scalar response variable for a given functional predictor. Compared with the conditional mean regression-based scalar-on-function regression model, the scalar-on-function quantile regression is robust to outliers in the response variable. However, it is susceptible to outliers in the functional predictor (called leverage points). The leverage points may alter the eigenstructure of the predictor matrix, leading to poor estimation and prediction results. A robust procedure is proposed to estimate the model parameters in the scalar-on-function quantile regression method and produce reliable predictions in the presence of both outliers and leverage points. The proposed method is based on a functional partial quantile regression procedure. The estimation and prediction performance of the proposed method is evaluated by a series of Monte-Carlo experiments and an empirical data example, diffusion tensor imaging data. The results are compared favorably with several existing methods. The method is implemented in an R package robfpqr.