On oracle efficiency of the ROAD classification rule

For high-dimensional classification Fishers rule performs poorly due to noise from estimation of the covariance matrix. Fan, Feng and Tong (2012) introduced the ROAD classifier that puts an $L_1$-constraint on the classification vector. In their Theorem 1 Fan, Feng and Tong (2012) show that the ROAD classifier asymptotically has the same misclassification rate as the corresponding oracle based classifier. Unfortunately, the proof contains an error. Here we restate the theorem and provide a new proof.