In partially linear model selection, Professor Chih-Ling Tsai and co-authors Hua Liang from the University of Rochester and Hansheng Wang from Peking University 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 the authors to obtain a uniform bound for the absolute difference between the profiled predictors and their estimators. Based on this finding, the study shows that the PFR algorithm uncovers all relevant variables within a few fairly short steps.