The Annals of Statistics

Test for bandedness of high-dimensional covariance matrices and bandwidth estimation

Yumou Qiu and Song Xi Chen

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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.

Article information

Ann. Statist., Volume 40, Number 3 (2012), 1285-1314.

First available in Project Euclid: 10 August 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62H15: Hypothesis testing
Secondary: 62G10: Hypothesis testing 62G20: Asymptotic properties

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


Qiu, Yumou; Chen, Song Xi. Test for bandedness of high-dimensional covariance matrices and bandwidth estimation. Ann. Statist. 40 (2012), no. 3, 1285--1314. doi:10.1214/12-AOS1002.

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