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

• 成果类型: Article
• 署名作者: Qiu, Yumou; Chen, Song Xi
• 署名单位: Iowa State University; Peking University; Peking University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/12-AOS1002
• 发表日期: 2012
• 页码: 1285-1314
• 关键词: largest eigenvalue; regularization; distributions; INDEPENDENCE; Lasso

摘要

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.