TEST FOR BANDEDNESS OF HIGH-DIMENSIONAL COVARIANCE MATRICES AND BANDWIDTH ESTIMATION

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.Statistics & ProbabilitySCI(E)0ARTICLE31285-13144