Law of log determinant of sample covariance matrix and optimal estimation of differential entropy for high-dimensional Gaussian distributions

[1]  V. Vu,et al.  Random matrices: Law of the determinant , 2011, 1112.0752.

[2]  Harrison H. Zhou,et al.  Optimal rates of convergence for estimating Toeplitz covariance matrices , 2013 .

[3]  Harrison H. Zhou,et al.  OPTIMAL RATES OF CONVERGENCE FOR SPARSE COVARIANCE MATRIX ESTIMATION , 2012, 1302.3030.

[4]  Harrison H. Zhou,et al.  MINIMAX ESTIMATION OF LARGE COVARIANCE MATRICES UNDER ℓ1-NORM , 2012 .

[5]  T. Tao,et al.  A central limit theorem for the determinant of a Wigner matrix , 2011, 1111.6300.

[6]  Harrison H. Zhou,et al.  Optimal rates of convergence for covariance matrix estimation , 2010, 1010.3866.

[7]  Maya R. Gupta,et al.  Parametric Bayesian Estimation of Differential Entropy and Relative Entropy , 2010, Entropy.

[8]  Alexandre B. Tsybakov,et al.  Introduction to Nonparametric Estimation , 2008, Springer series in statistics.

[9]  Maya R. Gupta,et al.  Bayesian estimation of the entropy of the multivariate Gaussian , 2008, 2008 IEEE International Symposium on Information Theory.

[10]  A. Rouault.  Asymptotic behavior of random determinants in the Laguerre, Gram and Jacobi ensembles , 2006, math/0607767.

[11]  Harshinder Singh,et al.  Estimation of the entropy of a multivariate normal distribution , 2005 .

[12]  T. Tao,et al.  On random ±1 matrices: Singularity and determinant , 2004, STOC '05.

[13]  Alfred O. Hero,et al.  Geodesic entropic graphs for dimension and entropy estimation in manifold learning , 2004, IEEE Transactions on Signal Processing.

[14]  Anja Vogler,et al.  An Introduction to Multivariate Statistical Analysis , 2004 .

[15]  Delannay,et al.  Distribution of the determinant of a random real-symmetric matrix from the gaussian orthogonal ensemble , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[16]  Jorgen Nielsen.  The distribution of volume reductions induced by isotropic random projections , 1999, Advances in Applied Probability.

[17]  A. M. Mathai.  Random p-content of a p-parallelotope in Euclidean n-space , 1999, Advances in Applied Probability.

[18]  V. Girko.  A Refinement of the Central Limit Theorem for Random Determinants , 1998 .

[19]  L. Györfi,et al.  Nonparametric entropy estimation. An overview , 1997 .

[20]  L. Brown,et al.  Information Inequality Bounds on the Minimax Risk (with an Application to Nonparametric Regression) , 1991 .

[21]  Vi︠a︡cheslav Leonidovich Girko,et al.  Theory of random determinants , 1990 .

[22]  D. V. Gokhale,et al.  Entropy expressions and their estimators for multivariate distributions , 1989, IEEE Trans. Inf. Theory.

[23]  Dag Jonsson.  Some limit theorems for the eigenvalues of a sample covariance matrix , 1982 .

[24]  R. Muirhead.  Aspects of Multivariate Statistical Theory , 1982, Wiley Series in Probability and Statistics.

[25]  V. Girko.  The Central Limit Theorem for Random Determinants , 1980 .

[26]  N. R. Goodman.  The Distribution of the Determinant of a Complex Wishart Distributed Matrix , 1963 .

[27]  T. MacRobert.  Higher Transcendental Functions , 1955, Nature.

[28]  A. Erdélyi,et al.  Higher Transcendental Functions , 1954 .