Condition-number-regularized covariance estimation

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 75, Issue 3, 2013, Pages 427-450

  Won, Joong Ho ^a   Lim, Johan ^b   Kim, Seung Jean ^c   Rajaratnam, Bala ^d  

^a Korea University   (South Korea)

^b Seoul National University   (South Korea)

^c Citi Capital Advisors   (United States)

^d STANFORD UNIVERSITY   (United States)

Author keywords

Condition number; Convex optimization; Covariance estimation; Cross validation; Eigenvalue; Portfolio optimization; Regularization; Risk comparisons; Shrinkage

Indexed keywords

EID: 84878257587     PISSN: 13697412     EISSN: 14679868     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2012.01049.x     Document Type: Article

References (33)

1. Banerjee, O., El Ghaoui, L. and D'Aspremont, A. (2008) Model selection through sparse maximum likelihood estimation for multivariate Gaussian or binary data. J. Mach. Learn. Res., 9, 485-516.
2. Boyd, S. and Vandenberghe, L. (2004) Convex Optimization. Cambridge: Cambridge University Press.
3. Chan, N., Karceski, N. and Lakonishok, J. (1999) On portfolio optimization: forecasting covariances and choosing the risk model. Rev. Finan. Stud., 12, 937-974.
4. Daniels, M. and Kass, R. (2001) Shrinkage estimators for covariance matrices. Biometrics, 57, 1173-1184.
5. Dempster, A. P. (1972) Covariance selection. Biometrics, 28, 157-175.
6. Dey, D. K. and Srinivasan, C. (1985) Estimation of a covariance matrix under Stein's loss. Ann. Statist., 13, 1581-1591.
7. Farrell, R. H. (1985) Multivariate Calculation. New York: Springer.
8. Friedman, J., Hastie, T. and Tibshirani, R. (2008) Sparse inverse covariance estimation with the graphical lasso. Biostatistics, 9, 432-441.
9. Haff, L. R. (1991) The variational form of certain Bayes estimators. Ann. Statist., 19, 1163-1190.
10. Hero, A. and Rajaratnam, B. (2011) Large-scale correlation screening. J. Am. Statist. Ass., 106, 1540-1552.
11. Hero, A. and Rajaratnam, B. (2012) Hub discovery in partial correlation graphs. IEEE Trans. Inform. Theor., 58, 6064-6078.
12. James, W. and Stein, C. (1961) Estimation with quadratic loss. In Proc. 4th Berkeley Symp. Mathematical Statistics and Probability, Stanford (ed. J. Neyman), pp. 361-379. Berkeley: University of California Press.
13. Khare, K. and Rajaratnam, B. (2011) Wishart distributions for decomposable covariance graph models.Ann. Statist., 39, 514-555.
14. Ledoit, O. and Wolf, M. (2003) Improved estimation of the covariance matrix of stock returns with an application to portfolio selection. J. Empir. Finan., 10, 603-621.
15. Ledoit, O. and Wolf, M. (2004) A well-conditioned estimator for large-dimensional covariance matrices. J. Multiv. Anal., 88, 365-411.
16. Ledoit, O. and Wolf, M. (2012) Nonlinear shrinkage estimation of large-dimensional covariance matrices. Ann. Statist., 40, 1024-1060.
17. Letac, G. and Massam, H. (2007) Wishart distributions for decomposable graphs. Ann. Statist., 35, 1278-1323.
18. Lin, S. and Perlman, M. (1985) A Monte-Carlo comparison of four estimators of a covariance matrix. Multiv. Anal., 6, 411-429.
19. Luenberger, D. G. (1998) Investment Science. New York: Oxford University Press.
20. Markowitz, H. (1952) Portfolio selection. J. Finan., 7, 77-91.
21. Merton, R. (1980) On estimating expected returns on the market: an exploratory investigation. J. Finan. Econ., 8, 323-361.
22. Michaud, R. O. (1989) The Markowitz optimization enigma: is optimized optimal. Finan. Anal. J., 45, 31-42.
23. Peng, J., Wang, P., Zhou, N. and Zhu, J. (2009) Partial correlation estimation by joint sparse regression models. J. Am. Statist. Ass., 104, 735-746.
24. Pourahmadi, M., Daniels, M. J. and Park, T. (2007) Simultaneous modelling of the cholesky decomposition of several covariance matrices. J. Multiv. Anal., 98, 568-587.
25. Rajaratnam, B., Massam, H. and Carvalho, C. (2008) Flexible covariance estimation in graphical Gaussian models. Ann. Statist., 36, 2818-2849.
26. Sheena, Y. and Gupta, A. (2003) Estimation of the multivariate normal covariance matrix under some restrictions. Statist. Decns, 21, 327-342.
27. Stein, C. (1956) Some problems in multivariate analysis Part I. Technical Report 6. Department of Statistics, Stanford University, Stanford.
28. Stein, C. (1975) Estimation of a covariance matrix. 39th A. Meet. Institute of Mathematical Statistics, Atlanta.
29. Stein, C. (1986) Lectures on the theory of estimation of many parameters (Engl. transl.). J. Math. Sci., 34, 1373-1403.
30. Tibshirani, R. (1996) Regression shrinkage and selection via the lasso. J. R. Statist. Soc. B, 58, 267-288.
31. Warton, D. I. (2008) Penalized normal likelihood and ridge regularization of correlation and covariance matrices. J. Am. Statist. Ass., 103, 340-349.
32. Won, J.-H. and Kim, S.-J. (2006) Maximum likelihood covariance estimation with a condition number constraint. In Proc. 40th Asilomar Conf. Signals, Systems and Computers, Pacific Grove, Oct. 29th-Nov. 1st (ed. M. B. Matthews), pp. 1445-1449. New York: Institute of Electrical and Electronics Engineers.
33. Yang, R. and Berger, J. O. (1994) Estimation of a covariance matrix using the reference prior. Ann. Statist., 22, 1195-1211.