Date of this Version
The Annals of Statistics
Testing covariance structure is of significant interest in many areas of statistical analysis and construction of compressed sensing matrices is an important problem in signal processing. Motivated by these applications, we study in this paper the limiting laws of the coherence of an n × p random matrix in the high-dimensional setting where p can be much larger than n. Both the law of large numbers and the limiting distribution are derived. 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. The limiting laws of the coherence of the data matrix play a critical role in the construction of the test. We also apply the asymptotic results to the construction of compressed sensing matrices.
Chen–Stein method, coherence, compressed sensing matrix, covariance structure, law of large numbers, limiting distribution, maxima, moderate deviations, mutual incoherence property, random matrix, sample correlation matrix
Cai, T., & Jiang, T. (2011). Limiting Laws of Coherence of Random Matrices With Applications to Testing Covariance Structure and Construction of Compressed Sensing Matrices. The Annals of Statistics, 39 (3), 1496-1525. http://dx.doi.org/10.1214/11-AOS879
Date Posted: 27 November 2017
This document has been peer reviewed.