# 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

See all articles by Chi Seng Pun

## Chi Seng Pun

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences

Date Written: April 23, 2019

### Abstract

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

Suggested Citation

Pun, Chi Seng and Hadimaja, Matthew Zakharia, A Self-Calibrated Direct Approach to Precision Matrix Estimation and Linear Discriminant Analysis in High Dimensions (April 23, 2019). Available at SSRN: https://ssrn.com/abstract=3422590 or http://dx.doi.org/10.2139/ssrn.3422590