Fluctuations of an improved population eigenvalue estimator in sample covariance matrix models

Details Fluctuations of an improved population eigenvalue estimator in sample covariance matrix models Fluctuations of an improved population eigenvalue estimator in sample covariance matrix models

2011-08-26

arxiv.org/abs/1108.5266v1

Mathematics

Probability

30 pp

Scientific paper

This article 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 known and 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. A specific application to wireless sensor networks is developed.

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