Open Access
June 2012 Test for bandedness of high-dimensional covariance matrices and bandwidth estimation
Yumou Qiu, Song Xi Chen
Ann. Statist. 40(3): 1285-1314 (June 2012). DOI: 10.1214/12-AOS1002


Motivated by the latest effort to employ banded matrices to estimate a high-dimensional covariance $\Sigma$, we propose a test for $\Sigma$ being banded with possible diverging bandwidth. The test is adaptive to the “large $p$, small $n$” situations without assuming a specific parametric distribution for the data. We also formulate a consistent estimator for the bandwidth of a banded high-dimensional covariance matrix. The properties of the test and the bandwidth estimator are investigated by theoretical evaluations and simulation studies, as well as an empirical analysis on a protein mass spectroscopy data.


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Yumou Qiu. Song Xi Chen. "Test for bandedness of high-dimensional covariance matrices and bandwidth estimation." Ann. Statist. 40 (3) 1285 - 1314, June 2012.


Published: June 2012
First available in Project Euclid: 10 August 2012

zbMATH: 1257.62064
MathSciNet: MR3015026
Digital Object Identifier: 10.1214/12-AOS1002

Primary: 62H15
Secondary: 62G10 , 62G20

Keywords: Banded covariance matrix , bandwidth estimation , high data dimension , large $p$ , nonparametric , small $n$

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 3 • June 2012
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