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A0397
Title: Non-crossing multiple-index quantile regression Authors:  Liping Zhu - Renmin University of China (China) [presenting]
Abstract: Though the theoretical properties of quantile regression have been extensively studied in the past three decades, in practice it is not unusual to obtain crossing quantile surfaces with regular approaches to estimating quantile functions at different quantile levels. The crossing quantile surfaces are intrinsically uninterpretable. To address this issue, we consider a semiparametric multi-index quantile regression subject to monotonicity restriction at different quantile levels. We first connect the semiparametric multi-index quantile regression model with a dimension-reducible model. Such a connection allows us to estimate the index coefficients consistently. The B-splines are then used to approximate the nonparametric function under the monotonicity restriction, which numerically corresponds to a constrained linear programming problem. To further improve efficiency, we estimate the B-spline coefficients based on a dual of linear programming. We assess the finite-sample performance of our proposed method through comprehensive simulations, and compare the prediction performance of different methods through an application to a real dataset.