High SNR Consistent Thresholding for Variable Selection

This work states and proves necessary and sufficient condition for a threshold based estimate of set of active regression coefficients to be high SNR consistent. It is further shown that popular thresholding schemes like universal threshold, Bonferroni correction etc fails to meet the necessary condition and hence are inconsistent at high SNR. The sufficient conditions provides a very rich class of threshold based estimators with varying rate of convergence to consistency. Simulation results demonstrates the superior performance of the proposed threshold based estimator over Lasso, Dantzig selector and Orthogonal Matching Pursuit.