Discussion of ‘Post selection shrinkage estimation for high-dimensional data analysis’

Researchers propose a post selection shrinkage estimation strategy to improve the prediction performance of a selected subset model. Such a post selection shrinkage estimator (PSE) is data adaptive and constructed by shrinking a post selection weighted ridge estimator in the direction of a selected candidate subset. Under an asymptotic distributional quadratic risk criterion, its prediction performance is explored analytically. The researchers show that the proposed post selection PSE performs better than the post selection weighted ridge estimator. It improves the prediction performance of any candidate subset model selected from most existing Lasso-type variable selection methods significantly. The relative performance of the post selection PSE is demonstrated by both simulation studies and real-data analysis.