Greedy Variable Screening in Ultra-high Dimensional Partially Linear Varying Coefficient Models

In this paper, the partially linear varying coefficient models were established when the predictors of the linear part were ultra-high dimensional, where the dimensionality grew exponentially with the sample size. A greedy profile forward regression (GPFR) method was proposed to finish the variable screening for the ultra-high dimensional linear predictors. Under some regularity conditions, the proposed GPFR method has a screening consistency property was proven. As for the GPFR procedure obtaining a list of the nested models, to determine whether or not to include the candidate predictor in the model of selected ones, an extended Bayesian information criterion (EBIC) was adopted to select the "best" candidate model. The finite-sample performance of the proposed GPFR method was assessed by using simulation studies and real data analysis. The result shows that the proposed GPFR method has advantage in the cases existing high correlation between the predictors and low signal noise ratio.