Testing the Diagonality of a Large Covariance Matrix in a Regression Setting

35 Pages Posted: 14 May 2014

See all articles by Wei Lan

Wei Lan

Peking University - Guanghua School of Management

Ronghua Luo

Southwestern University of Finance and Economics (SWUFE) - School of Finance

Chih-Ling Tsai

University of California, Davis - Graduate School of Management

Hansheng Wang

Peking University - Guanghua School of Management

Yunhong Yang

Peking University - Guanghua School of Management

Date Written: May 7, 2014

Abstract

In multivariate analysis, the covariance matrix associated with a set of variables of interest (namely response variables) commonly contains valuable information about the dataset. When the dimension of response variables is considerably larger than the sample size, it is a non-trivial task to assess whether they are linear relationships between the variables. It is even more challenging to determine whether a set of explanatory variables can explain those relationships. To this end, we develop a bias-corrected test to examine the significance of the off-diagonal elements of the residual covariance matrix after adjusting for the contribution from explanatory variables. We show that the resulting test is asymptotically normal. Monte Carlo studies and a numerical example are presented to illustrate the performance of the proposed test.

Keywords: Bias-Corrected Test; Covariance; Diagonality Test; High Dimensional Data; Multivariate Analysis

JEL Classification: C51, C52

Suggested Citation

Lan, Wei and Luo, Ronghua and Tsai, Chih-Ling and Wang, Hansheng and Yang, Yunhong, Testing the Diagonality of a Large Covariance Matrix in a Regression Setting (May 7, 2014). Available at SSRN: https://ssrn.com/abstract=2434355 or http://dx.doi.org/10.2139/ssrn.2434355

Wei Lan (Contact Author)

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871
China

Ronghua Luo

Southwestern University of Finance and Economics (SWUFE) - School of Finance ( email )

Chengdu, 610074
China

Chih-Ling Tsai

University of California, Davis - Graduate School of Management ( email )

One Shields Avenue
Davis, CA 95616
United States

Hansheng Wang

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871
China

HOME PAGE: http://hansheng.gsm.pku.edu.cn

Yunhong Yang

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871
China
8610-62768188 (Phone)

Register to save articles to
your library

Register

Paper statistics

Downloads
148
Abstract Views
917
rank
199,153
PlumX Metrics