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

Cai, T. Tony, Liang, Tengyuan, Zhou, Harrison H.·2015·Journal of Multivariate Analysis
DOI 10.1016/j.jmva.2015.02.003
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Research works printed but not linked: 24

  1. Ahmed, 1989, Entropy expressions and their estimators for multivariate distributions, IEEE Trans. Inform. Theory, 35, 688, 10.1109/18.30996 · DOI
  2. Beirlant, 1997, Nonparametric entropy estimation: an overview, Int. J. Math. Stat. Sci., 6, 17
  3. Brown, 1991, Information inequality bounds on the minimax risk (with an application to nonparametric regression), Ann. Statist., 19, 329, 10.1214/aos/1176347985 · DOI
  4. Cai, 2012, Optimal rates of convergence for estimating Toeplitz covariance matrices, Probab. Theory Related Fields, 1
  5. Cai, 2010, Optimal rates of convergence for covariance matrix estimation, Ann. Statist., 38, 2118, 10.1214/09-AOS752 · DOI
  6. Cai, 2011, Minimax estimation of large covariance matrices under ℓ−1 norm, Statist. Sinica
  7. Cai, 2012, Optimal rates of convergence for sparse covariance matrix estimation, Ann. Statist., 40, 2389, 10.1214/12-AOS998 · DOI
  8. Costa, 2004, Geodesic entropic graphs for dimension and entropy estimation in manifold learning, IEEE Trans. Signal Process., 52, 2210, 10.1109/TSP.2004.831130 · DOI
  9. Delannay, 2000, Distribution of the determinant of a random real-symmetric matrix from the Gaussian orthogonal ensemble, Phys. Rev. E, 62, 1526, 10.1103/PhysRevE.62.1526 · DOI
  10. Girko, 1980, The central limit theorem for random determinants, Theory Probab. Appl., 24, 729, 10.1137/1124086 · DOI
  11. Girko, 1998, A refinement of the central limit theorem for random determinants, Theory Probab. Appl., 42, 121, 10.1137/S0040585X97975939 · DOI
  12. Goodman, 1963, The distribution of the determinant of a complex Wishart distributed matrix, Ann. Math. Statist., 178, 10.1214/aoms/1177704251 · DOI · Paper page
  13. Gupta, 2010, Parametric Bayesian estimation of differential entropy and relative entropy, Entropy, 12, 818, 10.3390/e12040818 · DOI
  14. Jonsson, 1982, Some limit theorems for the eigenvalues of a sample covariance matrix, J. Multivariate Anal., 12, 1, 10.1016/0047-259X(82)90080-X · DOI
  15. Komlós, 1967, On the determinant of /0, 1/ matrices, Studia Sci. Math. Hungar., 2, 7
  16. Komlós, 1968, On the determinant of random matrices, Studia Sci. Math. Hungar., 3, 387
  17. Mathai, 1999, Random p-content of a p-parallelotope in euclidean n-space, Adv. Appl. Probab., 31, 343, 10.1239/aap/1029955138 · DOI
  18. Misra, 2005, Estimation of the entropy of a multivariate normal distribution, J. Multivariate Anal., 92, 324, 10.1016/j.jmva.2003.10.003 · DOI
  19. H.H. Nguyen, V. Vu, Random matrices: law of the determinant, 2011. ArXiv Preprint arXiv:1112.0752. · arXiv
  20. Nielsen, 1999, The distribution of volume reductions induced by isotropic random projections, Adv. Appl. Probab., 31, 985, 10.1239/aap/1029955254 · DOI
  21. A. Rouault, Asymptotic behavior of random determinants in the Laguerre, Gram and Jacobi ensembles, 2006. ArXiv Preprint arXiv:math/0607767. · arXiv
  22. S. Srivastava, M.R. Gupta, Bayesian estimation of the entropy of the multivariate Gaussian, in: IEEE International Symposium on Information Theory, 2008, pp. 1103–1107. · DOI
  23. Tao, 2006, On random ±1 matrices: singularity and determinant, Random Struct. Algorithms, 28, 1, 10.1002/rsa.20109 · DOI
  24. Tao, 2012, A central limit theorem for the determinant of a Wigner matrix, Adv. Math., 231, 74, 10.1016/j.aim.2012.05.006 · DOI

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Metadata

Authors
Cai, T. T., Liang, T., & Zhou, H. H.
Venue
Journal of Multivariate Analysis
Publisher
Elsevier BV
Published
2015-05
Volume
137
Pages
161-172
ISSN
0047-259X
DOI
10.1016/j.jmva.2015.02.003
Cited by
52
References
0
Language
en
Licence
Funders
  • NSF (DMS-0604954)
  • NSF FRG (DMS-0854973, DMS-0854975)
  • NSF Career Award (DMS-0645676)

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