Penalized Quantile Regression in Sparse High-dimensional Models
نویسندگان
چکیده
This paper studies high-dimensional parametric quantile regression models, where the dimension of the model increases with the sample size. we focus on the highdimensional low sample size (HDLSS) setting where the number of covariates is allowed to be larger than the sample size. The underlying assumption of the model that allows for a meaningful estimation is the sparseness of the true model. We consider estimation of either of these models using the a single quantile regression and the entire quantile regression processes. We establish consistency and rates of convergence of a penalized quantile regression. A data-driven choice of the penalization parameter is proposed and analyzed. We also establishes bounds on the number of nonzero coefficients of the estimated model. We illustrate the method numerically via a Monte carlo simulation and an empirical application. First Version: May 2, 2007 Last Revision: September 30, 2008
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