Department of Mathematics
Nonconcave penalized inverse regression in single-index models with high dimensional predictors
In this paper we aim to estimate the direction in general single-index models and to select important variables simultaneously when a diverging number of predictors are involved in regressions. Towards this end, we propose the nonconcave penalized inverse regression method. Specifically, the resulting estimation with the SCAD penalty enjoys an oracle property in semi-parametric models even when the dimension, pn, of predictors goes to infinity. Under regularity conditions we also achieve the asymptotic normality when the dimension of predictor vector goes to infinity at the rate of pn = o (n1 / 3) where n is sample size, which enables us to construct confidence interval/region for the estimated index. The asymptotic results are augmented by simulations, and illustrated by analysis of an air pollution dataset. © 2008 Elsevier Inc. All rights reserved.
62G20, 62H15, Dimension reduction, Diverging parameters, Inverse regression, SCAD, Sparsity
Source Publication Title
Journal of Multivariate Analysis
Link to Publisher's Edition
Zhu, Li-Ping, and Li-Xing Zhu. "Nonconcave penalized inverse regression in single-index models with high dimensional predictors." Journal of Multivariate Analysis 100.5 (2009): 862-875.