Additive Partially Linear Quantile Regression in Ultra-High Dimension

• Activity Number: 607
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Ben Sherwood* and Lan Wang
• Companies: The Johns Hopkins University and University of Minnesota
• Keywords: Quantile Regression ; high dimensional data ; non-convex penalty ; partial linear ; variable selection

Abstract

We consider flexible semiparametric quantile regression model for analyzing high dimensional heterogeneous data. This model has several appealing features: (1) By considering different conditional quantiles, we may obtain a more complete picture of the conditional distribution of a response variable given high dimensional covariates. (2) The sparsity level is allowed to be different at different quantile levels. (3) The partially linear additive structure accommodates nonlinearity and circumvents the curse of dimensionality. (4) It is naturally robust to heavy-tailed distributions. First we present estimation results for the oracle model, the model where the nonzero components of the linear covariates is known in advance. We then investigate a non-convex penalty for simultaneous variable selection of the linear components and estimation of the whole model. Proofs are provided demonstrating that the oracle model is asymptotically equivalent to the penalized estimator.