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Profiled Forward Regression for Ultrahigh Dimensional Variable Screening in Semiparametric Partially Linear Models

In partially linear model selection, we develop a profiled forward regression (PFR) algorithm for ultrahigh dimensional variable screening. The PFR algorithm effectively combines the ideas of nonparametric profiling and forward regression. This allows us to obtain a uniform bound for the absolute difference between the profiled predictors and their estimators. Based on this important finding, we are able to show that the PFR algorithm discovers all relevant variables within a few fairly short steps. Numerical studies are presented to illustrate the performance of the proposed method.