Rejoinder to ‘Post-selection shrinkage estimation for high-dimensional data analysis’

Rejoinder to the paper entitled ‘Post-selection shrinkage estimation for high-dimensional data analysis’ discusses different aspects of the study. One fundamental ingredient of the work is to formally split the signals into strong and weak ones. The rationale is that the usual one-step method such as the least absolute shrinkage and selection operator (LASSO) may be very effective in detecting strong signals while failing to identify some weak ones, which in turn has a significant impact on the model fitting, as well as prediction. The discussions of both Fan and QYY contain very interesting comments on the separation of the three sets of variables.