A Self-Calibrated Direct Approach to Precision Matrix Estimation and Linear Discriminant Analysis in High Dimensions
37 Pages Posted: 19 Jul 2019 Last revised: 6 Dec 2019
Date Written: April 23, 2019
This paper proposes a self-calibrated direct estimation algorithm based on ell1-regularized quadratic programming. 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. We consider two applications of this algorithm in this paper, namely precision matrix estimation and linear discriminant analysis. We prove the consistency results for the proposed estimators under different matrix norm errors and misclassification rate. Moreover, we conduct extensive simulation and empirical studies to evaluate the finite-sample performance and examine the support recovery ability of the proposed estimators. With the theoretical and empirical evidence, we show that the proposed estimator is better than its competitors in statistical accuracy and has clear computational advantages.
Keywords: High-dimensional statistics, Precision matrix estimation, Linear discriminant analysis, $\ell_1$-regularized quadratic programming, Self-calibrated regularization, Direct estimation approach
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