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Test for Bandedness of High Dimensional Covariance Matrices with Bandwidth Estimation

Qiu, Yumou and Chen, Songxi (2012): Test for Bandedness of High Dimensional Covariance Matrices with Bandwidth Estimation. Published in:

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Abstract

Motivated by the latest effort to employ banded matrices to estimate a high-dimensional covariance Σ , we propose a test for Σ 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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