Covariance structure regularization via entropy loss function

Computational Statistics and Data Analysis

Volumn 72, Issue , 2014, Pages 315-327

  Lin, Lijing ^a   Higham, Nicholas J ^a   Pan, Jianxin ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

Covariance estimation; Covariance structure; Entropy loss function; Kullback Leibler divergence; Regularization

Indexed keywords

COVARIANCE ESTIMATION; COVARIANCE STRUCTURES; ENTROPY LOSS FUNCTION; KULLBACK LEIBLER DIVERGENCE; REGULARIZATION;

ENTROPY; NEWTON-RAPHSON METHOD; STRUCTURAL OPTIMIZATION;

COVARIANCE MATRIX;

EID: 84890561743     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2013.10.004     Document Type: Article

References (21)

1. R. Borsdorf, N.J. Higham, and M. Raydan Computing a nearest correlation matrix with factor structure SIAM J. Matrix Anal. Appl. 31 5 2010 2603 2622
2. S. Boyd, and L. Vandenberghe Convex Optimization 2004 Cambridge University Press Cambridge, UK 978-0-521-83378-3
3. J.P. Burg, D.G. Luenberger, and D.L. Wenger Estimation of structured covariance matrices Proc. IEEE 70 9 1982 963 974
4. D.K. Dey, and C. Srinivasan Estimation of a covariance matrix under Stein's loss Ann. Statist. 13 4 1985 1581 1591
5. I.S. Dhillon, and J.A. Tropp Matrix nearness problems with Bregman divergences SIAM J. Matrix Anal. Appl. 29 4 2007 1120 1146
6. A. Ferrante, M. Pavon, and M. Zorzi A maximum entropy enhancement for a family of high-resolution spectral estimators IEEE Trans. Automat. Control 57 2 2012 318 329
7. N.J. Higham Accuracy and Stability of Numerical Algorithms second edition 2002 Society for Industrial and Applied Mathematics Philadelphia, PA, USA 0-89871-521-0
8. R.A. Horn, and C.R. Johnson Matrix Analysis second edition 2013 Cambridge University Press Cambridge, UK 978-0-521-83940-2
9. W. James, and C. Stein Estimation with quadratic loss J. Neyman, Proceedings of the Fourth Berkeley Symposium Mathematical Statistics and Probability vol. 1 1961 University of California Press 361 379 The Statistical Laboratory, University of California, June 30-July 30, 1960
10. M.G. Kenward A method for comparing profiles of repeated measurements Appl. Statist. 1987 296 308
11. F. Lin, and M.R. Jovanović Least-squares approximation of structured covariances IEEE Trans. Automat. Control 54 7 2009 1643 1648
12. E.M. Maboudou-Tchao, and V. Agboto Monitoring the covariance matrix with fewer observations than variables Comput. Statist. Data Anal. 64 2013 99 112
13. J.R. Magnus, and H. Neudecker Matrix Differential Calculus with Applications in Statistics and Econometrics revised edition 1999 Wiley Chichester, UK 0-471-98633-X
14. L. Ning, X. Jiang, and T. Georgiou Geometric methods for structured covariance estimation American Control Conference 2012 IEEE 1877 1882
15. J. Pan, and K. Fang Growth Curve Models and Statistical Diagnostics 2002 Springer-Verlag New York
16. J. Pan, and G. Mackenzie On modelling mean-covariance structures in longitudinal studies Biometrika 90 1 2003 239 244
17. S.V. Parter An observation on the numerical solution of difference equations and a theorem of Szegö Numer. Math. 4 1962 293 295
18. F. Pascal, Y. Chitour, J.P. Ovarlez, P. Forster, and P. Larzabal Covariance structure maximum-likelihood estimates in compound Gaussian noise: existence and algorithm analysis IEEE Trans. Signal Process. 56 1 2008 34 48
19. M. Pourahmadi Joint mean-covariance models with applications to longitudinal data: unconstrained parameterisation Biometrika 0006-3444 86 3 1999 677 690
20. V. Vinciotti, and H. Hashem Robust methods for inferring sparse network structures Comput. Statist. Data Anal. 67 2013 84 94
21. H. Ye, and J. Pan Modelling of covariance structures in generalised estimating equations for longitudinal data Biometrika 0006-3444 93 4 2006 927 941