Law of Log Determinant of Sample Covariance Matrix and Optimal Estimation of Differential Entropy for High-Dimensional Gaussian Distributions

@article{Cai2015LawOL,
  title={Law of Log Determinant of Sample Covariance Matrix and Optimal Estimation of Differential Entropy for High-Dimensional Gaussian Distributions},
  author={T. Tony Cai and Tengyuan Liang and Harrison H. Zhou},
  journal={J. Multivariate Analysis},
  year={2015},
  volume={137},
  pages={161-172}
}
Differential entropy and log determinant of the covariance matrix of a multivariate Gaussian distribution have many applications in coding, communications, signal processing and statistical inference. In this paper we consider in the high-dimensional setting optimal estimation of the differential entropy and the logdeterminant of the covariance matrix. We first establish a central limit theorem for the log determinant of the sample covariance matrix in the high-dimensional setting where the… CONTINUE READING
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