Profile Greedy Forward Regression Variable Screening for Ultra-High Dimensional Partially Linear Model

In this paper, we consider the ultra-high dimensional partially linear model, where the dimensionality p of linear component is much larger than the sample size n, and p can be as large as an exponential of the sample size n. Firstly, we transform the ultra-high dimensional partially linear model into the ultra-high dimensional linear model based the profile technique used in the semiparametric regression. Secondly, in order to finish the variable screening for high-dimensional linear component, we propose a variable screening method called as the profile greedy forward regression (PGFR) by combining the greedy algorithm with the forward regression (FR) method. The proposed PGFR method not only considers the correlation between the covariates, but also identifies all relevant predictors consistently and possesses the screening consistency property under the some regularity conditions. We further propose the BIC criterion to determine whether the selected model contains the true model with probability tending to one. Finally, some simulation studies and a real application are conducted to examine the finite sample performance of the proposed PGFR procedure.