메뉴 건너뛰기




Volumn 60, Issue 12, 2014, Pages 7874-7887

Calibrated precision matrix estimation for high-dimensional elliptical distributions

Author keywords

Calibrated Estimation; Elliptical Distribution; Heavy tailness; Precision Matrix; Semiparametric Model

Indexed keywords

SAMPLING;

EID: 84912119612     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/TIT.2014.2360980     Document Type: Article
Times cited : (23)

References (40)
  • 1
    • 41549101939 scopus 로고    scopus 로고
    • Model selection through sparse maximum likelihood estimation for multivariate Gaussian or binary data
    • Jun.
    • O. Banerjee, L. El Ghaoui, and A. d'Aspremont, "Model selection through sparse maximum likelihood estimation for multivariate Gaussian or binary data," J. Mach. Learn. Res., vol. 9, pp. 485-516, Jun. 2008.
    • (2008) J. Mach. Learn. Res. , vol.9 , pp. 485-516
    • Banerjee, O.1    El Ghaoui, L.2    D'aspremont, A.3
  • 2
    • 33745156863 scopus 로고    scopus 로고
    • Some theory for Fisher's linear discriminant function, 'naive Bayes', and some alternatives when there are many more variables than observations
    • P. J. Bickel and E. Levina, "Some theory for Fisher's linear discriminant function, 'naive Bayes', and some alternatives when there are many more variables than observations," Bernoulli, vol. 10, no. 6, pp. 989-1010, 2004.
    • (2004) Bernoulli , vol.10 , Issue.6 , pp. 989-1010
    • Bickel, P.J.1    Levina, E.2
  • 3
    • 52449116403 scopus 로고    scopus 로고
    • A correlated topic model of science
    • D. M. Blei and J. D. Lafferty, "A correlated topic model of science," Ann. Appl. Statist., vol. 1, no. 1, pp. 17-35, 2007.
    • (2007) Ann. Appl. Statist. , vol.1 , Issue.1 , pp. 17-35
    • Blei, D.M.1    Lafferty, J.D.2
  • 5
    • 79960110811 scopus 로고    scopus 로고
    • A constrained 1 minimization approach to sparse precision matrix estimation
    • T. Cai, W. Liu, and X. Luo, "A constrained 1 minimization approach to sparse precision matrix estimation," J. Amer. Statist. Assoc., vol. 106, no. 494, pp. 594-607, 2011.
    • (2011) J. Amer. Statist. Assoc. , vol.106 , Issue.494 , pp. 594-607
    • Cai, T.1    Liu, W.2    Luo, X.3
  • 6
    • 0000244379 scopus 로고
    • On the theory of elliptically contoured distributions
    • S. Cambanis, S. Huang, and G. Simons, "On the theory of elliptically contoured distributions," J. Multivariate Anal., vol. 11, no. 3, pp. 368-385, 1981.
    • (1981) J. Multivariate Anal. , vol.11 , Issue.3 , pp. 368-385
    • Cambanis, S.1    Huang, S.2    Simons, G.3
  • 7
    • 84879223772 scopus 로고    scopus 로고
    • Challenging the empirical mean and empirical variance: A deviation study
    • O. Catoni, "Challenging the empirical mean and empirical variance: A deviation study," Ann. Inst. Henri Poincaré Probab. Statist., vol. 48, no. 4, pp. 1148-1185, 2012.
    • (2012) Ann. Inst. Henri Poincaré Probab. Statist. , vol.48 , Issue.4 , pp. 1148-1185
    • Catoni, O.1
  • 8
    • 0001038826 scopus 로고
    • Covariance selection
    • A. P. Dempster, "Covariance selection," Biometrics, vol. 28, no. 1, pp. 157-175, 1972.
    • (1972) Biometrics , vol.28 , Issue.1 , pp. 157-175
    • Dempster, A.P.1
  • 11
    • 45849134070 scopus 로고    scopus 로고
    • Sparse inverse covariance estimation with the graphical lasso
    • J. Friedman, T. Hastie, and R. Tibshirani, "Sparse inverse covariance estimation with the graphical lasso," Biostatistics, vol. 9, no. 3, pp. 432-441, 2008.
    • (2008) Biostatistics , vol.9 , Issue.3 , pp. 432-441
    • Friedman, J.1    Hastie, T.2    Tibshirani, R.3
  • 13
    • 0023843391 scopus 로고
    • Analysis of hidden units in a layered network trained to classify sonar targets
    • R. P. Gorman and T. J. Sejnowski, "Analysis of hidden units in a layered network trained to classify sonar targets," Neural Netw., vol. 1, no. 1, pp. 75-89, 1988.
    • (1988) Neural Netw. , vol.1 , Issue.1 , pp. 75-89
    • Gorman, R.P.1    Sejnowski, T.J.2
  • 16
    • 85162490550 scopus 로고    scopus 로고
    • Sparse inverse covariance matrix estimation using quadratic approximation
    • Red Hook, NY, USA: Curran Associates
    • C.-J. Hsieh, I. S. Dhillon, P. K. Ravikumar, and M. A. Sustik, "Sparse inverse covariance matrix estimation using quadratic approximation," in Advances in Neural Information Processing Systems, vol. 24. Red Hook, NY, USA: Curran Associates, 2011, pp. 2330-2338.
    • (2011) Advances in Neural Information Processing Systems , vol.24 , pp. 2330-2338
    • Hsieh, C.-J.1    Dhillon, I.S.2    Ravikumar, P.K.3    Sustik, M.A.4
  • 17
    • 0036756224 scopus 로고    scopus 로고
    • Multivariate extremes, aggregation and dependence in elliptical distributions
    • H. Hult and F. Lindskog, "Multivariate extremes, aggregation and dependence in elliptical distributions," Adv. Appl. Probab., vol. 34, no. 3, pp. 587-608, 2002.
    • (2002) Adv. Appl. Probab. , vol.34 , Issue.3 , pp. 587-608
    • Hult, H.1    Lindskog, F.2
  • 18
    • 34248974445 scopus 로고
    • Ordinal measures of association
    • W. H. Kruskal, "Ordinal measures of association," J. Amer. Statist. Assoc., vol. 53, no. 284, pp. 814-861, 1958.
    • (1958) J. Amer. Statist. Assoc. , vol.53 , Issue.284 , pp. 814-861
    • Kruskal, W.H.1
  • 20
    • 73949122606 scopus 로고    scopus 로고
    • Sparsistency and rates of convergence in large covariance matrix estimation
    • C. Lam and J. Fan, "Sparsistency and rates of convergence in large covariance matrix estimation," Ann. Statist., vol. 37, no. 6B, pp. 4254-4278, 2009.
    • (2009) Ann. Statist. , vol.37 , Issue.6 B , pp. 4254-4278
    • Lam, C.1    Fan, J.2
  • 21
    • 0004047518 scopus 로고    scopus 로고
    • London, U.K.: Oxford Univ. Press
    • S. L. Lauritzen, Graphical Models, vol. 17. London, U.K.: Oxford Univ. Press, 1996.
    • (1996) Graphical Models , vol.17
    • Lauritzen, S.L.1
  • 22
    • 84912140286 scopus 로고    scopus 로고
    • The flare Package for Highdimensional Sparse Linear Regression in R
    • X. Li, T. Zhao, X. Yuan, and H. Liu, "The flare Package for Highdimensional Sparse Linear Regression in R," J. Mach. Learn. Res., 2014.
    • (2014) J. Mach. Learn. Res.
    • Li, X.1    Zhao, T.2    Yuan, X.3    Liu, H.4
  • 23
    • 84875151494 scopus 로고    scopus 로고
    • Highdimensional semiparametric Gaussian copula graphical models
    • H. Liu, F. Han, M. Yuan, J. Lafferty, and L. Wasserman, "Highdimensional semiparametric Gaussian copula graphical models," Ann. Statist., vol. 40, no. 4, pp. 2293-2326, 2012.
    • (2012) Ann. Statist. , vol.40 , Issue.4 , pp. 2293-2326
    • Liu, H.1    Han, F.2    Yuan, M.3    Lafferty, J.4    Wasserman, L.5
  • 25
    • 84879552585 scopus 로고    scopus 로고
    • TIGER: A tuning-insensitive approach for optimally estimating Gaussian graphical models
    • Cambridge, MA, USA, Tech. Rep.
    • H. Liu and L. Wang, "TIGER: A tuning-insensitive approach for optimally estimating Gaussian graphical models," Massachusett Inst. Technol., Cambridge, MA, USA, Tech. Rep., 2012.
    • (2012) Massachusett Inst. Technol.
    • Liu, H.1    Wang, L.2
  • 26
    • 84901751179 scopus 로고    scopus 로고
    • Sparse covariance matrix estimation with eigenvalue constraints
    • H. Liu, L. Wang, and T. Zhao, "Sparse covariance matrix estimation with eigenvalue constraints," J. Comput. Graph. Statist., vol. 23, no. 2, pp. 439-459, 2014.
    • (2014) J. Comput. Graph. Statist. , vol.23 , Issue.2 , pp. 439-459
    • Liu, H.1    Wang, L.2    Zhao, T.3
  • 27
    • 0010831555 scopus 로고
    • An approach to constructing optimal methods for minimization of smooth convex functions
    • Y. E. Nesterov, "An approach to constructing optimal methods for minimization of smooth convex functions," Èkonomika Matematicheskie Metody, vol. 24, no. 3, pp. 509-517, 1988.
    • (1988) Èkonomika Matematicheskie Metody , vol.24 , Issue.3 , pp. 509-517
    • Nesterov, Y.E.1
  • 28
    • 17444406259 scopus 로고    scopus 로고
    • Smooth minimization of non-smooth functions
    • Y. Nesterov, "Smooth minimization of non-smooth functions," Math. Program., vol. 103, no. 1, pp. 127-152, 2005.
    • (2005) Math. Program. , vol.103 , Issue.1 , pp. 127-152
    • Nesterov, Y.1
  • 29
  • 30
    • 80054725919 scopus 로고    scopus 로고
    • Sparse linear discriminant analysis by thresholding for high dimensional data
    • J. Shao, Y. Wang, X. Deng, and S. Wang, "Sparse linear discriminant analysis by thresholding for high dimensional data," Ann. Statist., vol. 39, no. 2, pp. 1241-1265, 2011.
    • (2011) Ann. Statist. , vol.39 , Issue.2 , pp. 1241-1265
    • Shao, J.1    Wang, Y.2    Deng, X.3    Wang, S.4
  • 32
    • 84869449202 scopus 로고    scopus 로고
    • Scaled sparse linear regression
    • T. Sun and C. Zhang, "Scaled sparse linear regression," Biometrika, vol. 99, no. 4, p. 879, 2012.
    • (2012) Biometrika , vol.99 , Issue.4 , pp. 879
    • Sun, T.1    Zhang, C.2
  • 35
    • 84972514544 scopus 로고
    • Discriminant analysis under elliptical populations
    • H. Wakaki, "Discriminant analysis under elliptical populations," Hiroshima Math. J., vol. 24, no. 2, pp. 257-298, 1994.
    • (1994) Hiroshima Math. J. , vol.24 , Issue.2 , pp. 257-298
    • Wakaki, H.1
  • 36
    • 22044448669 scopus 로고    scopus 로고
    • Sparse graphical Gaussian modeling of the isoprenoid gene network in arabidopsis thaliana
    • A. Wille et al., "Sparse graphical Gaussian modeling of the isoprenoid gene network in arabidopsis thaliana," Genome Biol., vol. 25, no. 5, p. R92, 2004.
    • (2004) Genome Biol. , vol.25 , Issue.5 , pp. R92
    • Wille, A.1
  • 37
    • 77956916683 scopus 로고    scopus 로고
    • High dimensional inverse covariance matrix estimation via linear programming
    • Mar.
    • M. Yuan, "High dimensional inverse covariance matrix estimation via linear programming," J. Mach. Learn. Res., vol. 11, pp. 2261-2286, Mar. 2010.
    • (2010) J. Mach. Learn. Res. , vol.11 , pp. 2261-2286
    • Yuan, M.1
  • 38
    • 33947115409 scopus 로고    scopus 로고
    • Model selection and estimation in the Gaussian graphical model
    • M. Yuan and Y. Lin, "Model selection and estimation in the Gaussian graphical model," Biometrika, vol. 94, no. 1, pp. 19-35, 2007.
    • (2007) Biometrika , vol.94 , Issue.1 , pp. 19-35
    • Yuan, M.1    Lin, Y.2
  • 39
    • 85048459956 scopus 로고    scopus 로고
    • Sparse inverse covariance estimation with calibration
    • Red Hook, NY, USA: Curran Associates
    • T. Zhao and H. Liu, "Sparse inverse covariance estimation with calibration," in Advances in Neural Information Processing Systems 26. Red Hook, NY, USA: Curran Associates, 2013.
    • (2013) Advances in Neural Information Processing Systems , vol.26
    • Zhao, T.1    Liu, H.2
  • 40
    • 84860650411 scopus 로고    scopus 로고
    • The huge package for high-dimensional undirected graph estimation in R
    • T. Zhao, H. Liu, K. Roeder, J. Lafferty, and L. Wasserman, "The huge package for high-dimensional undirected graph estimation in R," J. Mach. Learn. Res., vol. 13, no. 1, pp. 1059-1062, 2012.
    • (2012) J. Mach. Learn. Res. , vol.13 , Issue.1 , pp. 1059-1062
    • Zhao, T.1    Liu, H.2    Roeder, K.3    Lafferty, J.4    Wasserman, L.5


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.