Nonparametric quantile regression models via majorization minimization-algorithm

In this paper, we apply the Majorization Minimization (MM)-algorithm to deal with the computational problem of the smoothing nonparametric quantile regression. We show that the proposed MM-algorithm possesses the descent property, and the estimator obtained by the proposed algorithm is smooth. Simulation studies demonstrate that the estimator based on our proposed method is more robust and efficient than the estimator based on the mean smoothing regression and the estimator proposed by Nychka et al. (1995) with GCV scores. Finally, we apply the proposed methodology to analyze the dataset about bone density (BMD) in adolescents.

Keywords

MM-algorithm, nonparametric quantile regression, robustness

2010 Mathematics Subject Classification

Primary 62F35. Secondary 62G08.

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Published 17 April 2014