Robust Linear Discriminant Analysis Using Tyler's Estimator: Asymptotic Performance Characterization

We consider a robust version of regularized discriminant analysis (RDA) classifiers to account for potential spurious or mislabeled observations in the training data set. To build a robust discriminant rule, a robust estimation of the covariance matrix is essential. In this work, we propose to use a regularized version of Tyler's covariance estimator, in the regime where both the number of variables and the number of training samples are large and of similar order. Building upon fundamental results from random matrix theory, we show that the robust classifier is asymptotically equivalent to traditional, non-robust classifiers when the training data is free from outliers. Simulations on synthetic and real datasets confirm our theoretical observations and further attest to the benefits brought by the robust classifier when the data is corrupted by outliers.