Title: Sparse smooth backfitting for high-dimensional additive regression
Authors: Eun Ryung Lee - Sungkyunkwan University (Korea, South) [presenting]
Abstract: Smooth backtting methods have been proposed and proven as a powerful nonparametric estimation technique for additive regression models in various settings. However, such established studies are restricted to cases with a moderate number of predictors and the existing methods are not directly applicable to high dimensional settings. We develop a new kernel estimator based on smooth backfitting that works in high dimensional additive models. For this, we develop novel penalizations of functional LASSO and its weighted version then they will be applied to smooth backtting methods. We provide oracle results about the resulting penalized smooth backtting methods. In order to implement the new estimators, we derive a numerical algorithm of iteratively applying (componentwise) thresholding operators and present its improved version for a more accurate and efficient computation. Further, we suggest a BIC-type criterion for choosing the penalization parameters.