A self-calibrated direct approach to precision matrix estimation and linear discriminant analysis in high dimensions

Abstract

A self-calibrated direct estimation algorithm based on ℓ1-regularized quadratic programming is proposed. The self-calibration is achieved by an iterative algorithm for finding the regularization parameter simultaneously with the estimation target. The proposed algorithm is free of cross-validation. Two applications of this algorithm are proposed, namely precision matrix estimation and linear discriminant analysis. It is proven that the proposed estimators are consistent under different matrix norm errors and misclassification rate. Moreover, extensive simulation and empirical studies are conducted to evaluate the finite-sample performance and examine the support recovery ability of the proposed estimators. With the theoretical and empirical evidence, it is shown that the proposed estimator is better than its competitors in statistical accuracy and has clear computational advantages.