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:

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Banded covariance matrix,Bandwidth estimation,High data dimension,Large p,small n,Nonparametric.
• Subjects: C - Mathematical and Quantitative Methods > C0 - General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory; C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs; C - Mathematical and Quantitative Methods > C9 - Design of Experiments; G - Financial Economics > G0 - General

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