On oracle efficiency of the ROAD classification rule

TL;DR

This paper revisits the theoretical properties of the ROAD classifier in high-dimensional classification, correcting a proof error in previous work and establishing its asymptotic oracle efficiency.

Contribution

The authors provide a new proof for the oracle efficiency of the ROAD classifier, clarifying its theoretical performance in high-dimensional settings.

Findings

Theorem 1 is restated with a corrected proof.

ROAD classifier asymptotically matches the oracle classifier's misclassification rate.

The paper confirms the robustness of the ROAD classifier's theoretical properties.

Abstract

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.