Fluctuations of an Improved Population Eigenvalue Estimator in Sample Covariance Matrix Models

• Published in: IEEE transactions on information theory Vol. 59; no. 2; pp. 1149 - 1163
• Main Authors: Jianfeng Yao, Couillet, R., Najim, J., Debbah, M.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-02-2013; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Central limit theorem; Computer Science; Convergence; Covariance matrices; eigenvalue estimators; Eigenvalues; Eigenvalues and eigenfunctions; Estimation theory; Exact sciences and technology; G-estimation; Information Theory; Information, signal and communications theory; Mathematical models; Mathematics; Matrix; Probability; random matrix theory; Sample size; Statistics; Statistics Theory; Stieltjes transform; Telecommunications and information theory; Theorems; G-estimation; Random matrix; Central limit theorem; eigenvalue estimators; Covariance; Simulation; Eigenvalue; random matrix theory; Covariance matrix; Stieltjes transform; large random matrices; population matrix estimation; wireless communication
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2012.2222862

This paper provides a central limit theorem for a consistent estimator of population eigenvalues with large multiplicities based on sample covariance matrices. The focus is on limited sample size situations, whereby the number of available observations is comparable in magnitude to the observation dimension. An exact expression as well as an empirical, asymptotically accurate, approximation of the limiting variance is derived. Simulations are performed that corroborate the theoretical claims.