Positive Definite Estimation of Large Covariance Matrix Using Generalized Nonconvex Penalties

04/15/2016
by   Fei Wen, et al.
0

This work addresses the issue of large covariance matrix estimation in high-dimensional statistical analysis. Recently, improved iterative algorithms with positive-definite guarantee have been developed. However, these algorithms cannot be directly extended to use a nonconvex penalty for sparsity inducing. Generally, a nonconvex penalty has the capability of ameliorating the bias problem of the popular convex lasso penalty, and thus is more advantageous. In this work, we propose a class of positive-definite covariance estimators using generalized nonconvex penalties. We develop a first-order algorithm based on the alternating direction method framework to solve the nonconvex optimization problem efficiently. The convergence of this algorithm has been proved. Further, the statistical properties of the new estimators have been analyzed for generalized nonconvex penalties. Moreover, extension of this algorithm to covariance estimation from sketched measurements has been considered. The performances of the new estimators have been demonstrated by both a simulation study and a gene clustering example for tumor tissues. Code for the proposed estimators is available at https://github.com/FWen/Nonconvex-PDLCE.git.

READ FULL TEXT

page 8

page 10

page 11

research
01/01/2018

Ensemble Estimation of Large Sparse Covariance Matrix Based on Modified Cholesky Decomposition

Estimation of large sparse covariance matrices is of great importance fo...
research
03/20/2018

Sparse Reduced Rank Regression With Nonconvex Regularization

In this paper, the estimation problem for sparse reduced rank regression...
research
03/02/2019

Matrix Completion via Nonconvex Regularization: Convergence of the Proximal Gradient Algorithm

Matrix completion has attracted much interest in the past decade in mach...
research
10/22/2020

Positive definiteness of the asymptotic covariance matrix of OLS estimators in parsimonious regressions

Recently, Ghysels, Hill, and Motegi (2020) proposed a test for examining...
research
11/22/2017

Sparsity-based Cholesky Factorization and its Application to Hyperspectral Anomaly Detection

Estimating large covariance matrices has been a longstanding important p...
research
04/17/2023

Sparse Positive-Definite Estimation for Large Covariance Matrices with Repeated Measurements

In many fields of biomedical sciences, it is common that random variable...
research
04/06/2022

A novel nonconvex, smooth-at-origin penalty for statistical learning

Nonconvex penalties are utilized for regularization in high-dimensional ...

Please sign up or login with your details

Forgot password? Click here to reset