A New Statistics for Testing Covariance Struture of the High-Dimension Random Vector

• Activity Number: 136
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
• Sponsor: International Chinese Statistical Association
• Author(s): Danning Li*+ and Tiefeng Jiang
• Companies: University of Minnesota and University of Minnesota
• Keywords: Covariance Structure ; Berry_Essen Bound ; Chen_Stein Method ; Moderate deviation ; Random Matrix ; Sample Correlation mareix

Abstract

Testing covariance structure is of significant interest in many areas of statistical analysis. Motivated by these applications, we use another statistic instead of the coherence statistic for testing independence if the $p$-variates of the population and prove the law of large numbers and the limiting distribution under setting where $p$ can be much larger than $n$. We also obtain $O(\frac{\log p^{3/2}}{n^{1/2}})$, which is much faster than $O(\frac{1}{\log n})$. We then consider testing the bandedness of the covariance matrix of a high dimensional Gaussian distribution which includes testing for independence as a special case.