title: Calibrated Precision Matrix Estimation for High-Dimensional Elliptical Distributions.
abstract: We propose a semiparametric method for estimating a precision matrix of high-dimensional elliptical distributions. Unlike most existing methods, our method naturally handles heavy tailness and conducts parameter estimation under a calibration framework, thus achieves improved theoretical rates of convergence and finite sample performance on heavy-tail applications. We further demonstrate the performance of the proposed method using thorough numerical experiments.
authors: Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ 08544 USA, and also with the Department of Computer Science, Johns Hopkins University, Baltimore, MD 21218 USA ( tour@cs.jhu.edu ).
authors: Tuo
authors: T
authors: Zhao
authors: Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ 08544 USA ( hanliu@princeton.edu ).
authors: Han
authors: H
authors: Liu
keywords: Precision matrix; calibrated estimation; elliptical distribution; heavy-tailness; semiparametric model
references: Genome Biol. 2004;5(11):R92
references: 15535868
references: Biostatistics. 2008 Jul;9(3):432-41
references: 18079126
references: Ann Stat. 2009;37(6B):4254-4278
references: 21132082
references: J Comput Graph Stat. 2014 Apr;23(2):439-459
references: 25620866
references: J Mach Learn Res. 2012 Apr;13:1059-1062
references: 26834510
references: J Mach Learn Res. 2015 Mar;16:553-557
references: 28337074