title: SEMIPARAMETRIC QUANTILE REGRESSION WITH HIGH-DIMENSIONAL COVARIATES.
abstract: This paper is concerned with quantile regression for a semiparametric regression model, in which both the conditional mean and conditional variance function of the response given the covariates admit a single-index structure. This semiparametric regression model enables us to reduce the dimension of the covariates and simultaneously retains the flexibility of nonparametric regression. Under mild conditions, we show that the simple linear quantile regression offers a consistent estimate of the index parameter vector. This is a surprising and interesting result because the single-index model is possibly misspecified under the linear quantile regression. With a root-nconsistent estimate of the index vector, one may employ a local polynomial regression technique to estimate the conditional quantile function. This procedure is computationally efficient, which is very appealing in high-dimensional data analysis. We show that the resulting estimator of the quantile function performs asymptotically as efficiently as if the true value of the index vector were known. The methodologies are demonstrated through comprehensive simulation studies and an application to a real dataset.
authors: School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, 200433, P. R. China.
authors: Liping
authors: L
authors: Zhu
authors: School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, 200433, P. R. China.
authors: Mian
authors: M
authors: Huang
authors: Department of Statistics and The Methodology Center, The Pennsylvania State University, University Park, Pennsylvania, 16802-2111, USA.
authors: Runze
authors: R
authors: Li
keywords: Dimension reduction; heteroscedasticity; linearity condition; local polynomial regression; quantile regression; single-index model