Statistical consistency of coefficient-based conditional quantile regression

Jia Cai and Dao-Hong Xiang

Journal of Multivariate Analysis, 2016, vol. 149, issue C, 1-12

Abstract: This study focuses on the coefficient-based conditional quantile regression associated with lq-regularization term, where 1≤q≤2. Error analysis is investigated based on the capacity of the hypothesis space. The linear piecewise nature of the pinball loss function for quantile regression and the lq-penalty of the learning algorithm lead to some difficulties in the theoretical analysis. In order to overcome the difficulties, we introduce a novel error decomposition formula. The prolix iteration is then circumvented in the error analysis. Some satisfactory learning rates are achieved in a general setting under mild conditions.

Keywords: Learning theory; Quantile regression; Reproducing kernel Hilbert space (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.jmva.2016.03.006

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