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Volumn 59, Issue 9, 2011, Pages 4097-4107

Robust shrinkage estimation of high-dimensional covariance matrices

Author keywords

Activity intrusion detection; covariance estimation; elliptical distribution; large p small n; robust estimation; shrinkage methods; wireless sensor network

Indexed keywords

COVARIANCE ESTIMATION; ELLIPTICAL DISTRIBUTION; LARGE P SMALL N; ROBUST ESTIMATION; WIRELESS SENSOR;

EID: 80051725450     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2011.2138698     Document Type: Article
Times cited : (205)

References (38)
  • 1
    • 34249722106 scopus 로고
    • Estimation of a covariance matrix
    • presented at the Rietz Lecture, IMS, Atlanta, GA
    • C. Stein, "Estimation of a covariance matrix," presented at the Rietz Lecture, 39th Annu. Meeting, IMS, Atlanta, GA, 1975.
    • (1975) 39th Annu. Meeting
    • Stein, C.1
  • 2
    • 0346961488 scopus 로고    scopus 로고
    • A well-conditioned estimator for large-dimensional covariance matrices
    • DOI 10.1016/S0047-259X(03)00096-4
    • O. Ledoit and M. Wolf, "A well-conditioned estimator for large-dimensional covariance matrices," J. Multivar. Anal., vol. 88, no. 2, pp. 365-411, Feb. 2004. (Pubitemid 38033261)
    • (2004) Journal of Multivariate Analysis , vol.88 , Issue.2 , pp. 365-411
    • Ledoit, O.1    Wolf, M.2
  • 3
    • 77956726241 scopus 로고    scopus 로고
    • Shrinkage algorithms forMMSEcovariance estimation
    • Oct
    • Y. Chen, A.Wiesel, Y. C. Eldar, and A. O. Hero, III, "Shrinkage algorithms forMMSEcovariance estimation," IEEE Trans. Signal Process., vol. 58, no. 10, pp. 5016-5029, Oct. 2010.
    • (2010) IEEE Trans. Signal Process. , vol.58 , Issue.10 , pp. 5016-5029
    • Chen, Y.1    Wiesel, A.2    Eldar, Y.C.3    Hero III, A.O.4
  • 4
    • 45849134070 scopus 로고    scopus 로고
    • Sparse inverse covariance estimation with the graphical lasso
    • DOI 10.1093/biostatistics/kxm045
    • J. Friedman, T. Hastie, and R. Tibshirani, "Sparse inverse covariance estimation with the graphical lasso," Biostatistics, vol. 9, no. 3, pp. 432-441, 2008. (Pubitemid 351882084)
    • (2008) Biostatistics , vol.9 , Issue.3 , pp. 432-441
    • Friedman, J.1    Hastie, T.2    Tibshirani, R.3
  • 5
    • 41549106844 scopus 로고    scopus 로고
    • Regularized estimation of large covariance matrices
    • P. Bickel and E. Levina, "Regularized estimation of large covariance matrices," Ann. Stat., vol. 36, pp. 199-227, 2008.
    • (2008) Ann. Stat. , vol.36 , pp. 199-227
    • Bickel, P.1    Levina, E.2
  • 6
    • 0035641726 scopus 로고    scopus 로고
    • On the distribution of the largest eigenvalue in principal components analysis
    • I. M. Jonestone, "On the distribution of the largest eigenvalue in principal components analysis," Ann. Stat., vol. 29, pp. 295-327, 2001.
    • (2001) Ann. Stat. , vol.29 , pp. 295-327
    • Jonestone, I.M.1
  • 7
    • 0001248728 scopus 로고
    • Distribution theory of spherical distributions and a location-scale parameter generalization
    • D. Kelker, "Distribution theory of spherical distributions and a location-scale parameter generalization," Sankhya, vol. A32, pp. 419-430, 1970.
    • (1970) Sankhya , vol.A32 , pp. 419-430
    • Kelker, D.1
  • 9
    • 0000342767 scopus 로고
    • A distribution-free M-estimator of multivariate scatter
    • D. E. Tyler, "A distribution-free M-estimator of multivariate scatter," Ann. Stat., vol. 15, no. 1, pp. 234-251, 1987.
    • (1987) Ann. Stat. , vol.15 , Issue.1 , pp. 234-251
    • Tyler, D.E.1
  • 10
    • 0002564033 scopus 로고
    • Multivariate estimation with high breakdown point
    • Amsterdam, The Netherlands: Reidel
    • P. Rousseeuw, "Multivariate estimation with high breakdown point," in Mathematical Statistics and Applications. Amsterdam, The Netherlands: Reidel, 1985, vol. B, pp. 283-297.
    • (1985) Mathematical Statistics and Applications , vol.B , pp. 283-297
    • Rousseeuw, P.1
  • 12
    • 0002452734 scopus 로고
    • Adaptive radar detection in compound-Gaussian clutter
    • Edinburgh, U.K., Sep
    • E. Conte, M. Lops, and G. Ricci, "Adaptive radar detection in compound-Gaussian clutter," in Proc. EUSIPCO, Edinburgh, U.K., Sep. 1994, pp. 526-529.
    • (1994) Proc. EUSIPCO , pp. 526-529
    • Conte, E.1    Lops, M.2    Ricci, G.3
  • 13
    • 0029291208 scopus 로고
    • Asymptotically optimum radar detection in compound-Gaussian clutter
    • Apr
    • E. Conte, M. Lops, and G. Ricci, "Asymptotically optimum radar detection in compound-Gaussian clutter," IEEE Trans. Aerosp. Electron. Syst., vol. 31, pp. 617-625, Apr. 1995.
    • (1995) IEEE Trans. Aerosp. Electron. Syst. , vol.31 , pp. 617-625
    • Conte, E.1    Lops, M.2    Ricci, G.3
  • 14
    • 0036683911 scopus 로고    scopus 로고
    • Recursive estimation of the covariance matrix of a compound-Gaussian process and its application to adaptive CFAR detection
    • Aug
    • E. Conte, A. De Maio, and G. Ricci, "Recursive estimation of the covariance matrix of a compound-Gaussian process and its application to adaptive CFAR detection," IEEE Trans. Signal Process., vol. 50, no. 8, pp. 1908-1915, Aug. 2002.
    • (2002) IEEE Trans. Signal Process. , vol.50 , Issue.8 , pp. 1908-1915
    • Conte, E.1    De Maio, A.2    Ricci, G.3
  • 15
    • 0031069693 scopus 로고    scopus 로고
    • Sub-optimum coherent radar detection in a mixture of Kdistributed and Gaussian clutter
    • Feb
    • F. Gini, "Sub-optimum coherent radar detection in a mixture of Kdistributed and Gaussian clutter," Proc. Inst. Electr. Eng.-Radar, Sonar, Navig., vol. 144, no. 1, pp. 39-48, Feb. 1997.
    • (1997) Proc. Inst. Electr. Eng.-Radar, Sonar, Navig. , vol.144 , Issue.1 , pp. 39-48
    • Gini, F.1
  • 16
    • 0036887912 scopus 로고    scopus 로고
    • Covariance matrix estimation for CFAR detection in correlated heavy tailed clutter
    • DOI 10.1016/S0165-1684(02)00315-8, PII S0165168402003158
    • F. Gini and M. V. Greco, "Covariance matrix estimation for CFAR detection in correlated heavy tailed clutter," Signal Process. (Special Section on Signal Processing with Heavy Tailed Distributions), vol. 82, no. 12, pp. 1847-1859, Dec. 2002. (Pubitemid 35214244)
    • (2002) Signal Processing , vol.82 , Issue.12 , pp. 1847-1859
    • Gini, F.1    Greco, M.2
  • 17
    • 33749376774 scopus 로고    scopus 로고
    • Maximum likelihood estimation of compound-Gaussian clutter and target parameters
    • DOI 10.1109/TSP.2006.880209
    • J.Wang, A. Dogandzic, and A. Nehorai, "Maximum likelihood estimation of compound-Gaussian clutter and target parameters," IEEE Trans. Signal Process., vol. 54, no. 10, pp. 3884-3898, Oct. 2006. (Pubitemid 44500841)
    • (2006) IEEE Transactions on Signal Processing , vol.54 , Issue.10 , pp. 3884-3898
    • Wang, J.1    Dogandzic, A.2    Nehorai, A.3
  • 18
    • 37749041370 scopus 로고    scopus 로고
    • Covariance structure maximum-likelihood estimates in compound Gaussian noise: Existence and algorithm analysis
    • Jan
    • 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., vol. 56, no. 1, pp. 34-48, Jan. 2008.
    • (2008) IEEE Trans. Signal Process. , vol.56 , Issue.1 , pp. 34-48
    • Pascal, F.1    Chitour, Y.2    Ovarlez, J.-P.3    Forster, P.4    Larzabal, P.5
  • 19
    • 53149152990 scopus 로고    scopus 로고
    • Exact maximum likelihood estimates for SIRV covariance matrix: Existence and algorithm analysis
    • Oct
    • Y. Chitour and F. Pascal, "Exact maximum likelihood estimates for SIRV covariance matrix: Existence and algorithm analysis," IEEE Trans. Signal Process., vol. 56, no. 10, pp. 4563-4573, Oct. 2008.
    • (2008) IEEE Trans. Signal Process. , vol.56 , Issue.10 , pp. 4563-4573
    • Chitour, Y.1    Pascal, F.2
  • 20
    • 20544451350 scopus 로고    scopus 로고
    • Statistical analysis of the nonhomogeneity detector for non-Gaussian interference backgrounds
    • DOI 10.1109/TSP.2005.847843
    • M. Rangaswamy, "Statistical analysis of the nonhomogeneity detector for non-Gaussian interference backgrounds," IEEE Trans. Signal Process., vol. 53, no. 6, pp. 2101-2111, Jun. 2005. (Pubitemid 40843766)
    • (2005) IEEE Transactions on Signal Processing , vol.53 , Issue.6 , pp. 2101-2111
    • Rangaswamy, M.1
  • 21
    • 34547511794 scopus 로고    scopus 로고
    • Diagonally loaded normalised sample matrix inversion (LNSMI) for outlier-resistant adaptive filtering
    • Y. I. Abramovich and N. K. Spencer, "Diagonally loaded normalised sample matrix inversion (LNSMI) for outlier-resistant adaptive filtering," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., 2007, vol. 3, pp. 1105-1108.
    • (2007) Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. , vol.3 , pp. 1105-1108
    • Abramovich, Y.I.1    Spencer, N.K.2
  • 22
    • 0009066318 scopus 로고
    • Ground clutter measurements for surface-sited radar
    • Feb
    • J. B. Billingsley, "Ground clutter measurements for surface-sited radar," MIT, Tech. Rep. 780, Feb. 1993.
    • (1993) MIT, Tech. Rep. , vol.780
    • Billingsley, J.B.1
  • 23
    • 0023313586 scopus 로고
    • Description and generation of spherically invariant speech-model signals
    • DOI 10.1016/0165-1684(87)90001-6
    • H. Brehm and W. Stammler, "Description and generation of spherically invariant speech-model signals," Signal Process., vol. 12, no. 2, pp. 119-141, Mar. 1987. (Pubitemid 17572792)
    • (1987) Signal Processing , vol.12 , Issue.2 , pp. 119-141
    • Brehm, H.1    Stammler, W.2
  • 24
    • 67649790793 scopus 로고    scopus 로고
    • Normalized coherency matrix estimation under the SIRV model. Alpine glacier polsar data analysis
    • G. Vasile et al., "Normalized coherency matrix estimation under the SIRV model. Alpine glacier polsar data analysis," in Proc. IEEE Int. Geosci. Remote Sens. Symp., 2008, vol. 1, pp. 74-77.
    • (2008) Proc. IEEE Int. Geosci. Remote Sens. Symp. , vol.1 , pp. 74-77
    • Vasile, G.1
  • 25
    • 23444451371 scopus 로고    scopus 로고
    • Generalized elliptical distributions: Theory and applications
    • Ph.D. dissertation,. Dept., Univ. of Cologne, Cologne, Germany
    • G. Frahm, "Generalized elliptical distributions: Theory and applications," Ph.D. dissertation, Economic and Social Statist. Dept., Univ. of Cologne, Cologne, Germany, 2004.
    • (2004) Economic and Social Statist
    • Frahm, G.1
  • 26
    • 0015662367 scopus 로고
    • A representation theorem and its applications to spherically invariant random processes
    • Sep
    • K. Yao, "A representation theorem and its applications to spherically invariant random processes," IEEE Trans. Inf. Theory, vol. IT-19, pp. 600-608, Sep. 1973.
    • (1973) IEEE Trans. Inf. Theory , vol.IT-19 , pp. 600-608
    • Yao, K.1
  • 28
    • 0000672652 scopus 로고
    • Relative stability for ascending and positively homogeneous operators on Banach spaces
    • U. Krause, "Relative stability for ascending and positively homogeneous operators on Banach spaces," J. Math. Anal. Appl., pp. 182-202, 1994.
    • (1994) J. Math. Anal. Appl. , pp. 182-202
    • Krause, U.1
  • 29
    • 0035424189 scopus 로고    scopus 로고
    • Concave Perron-Frobenius theory and applications
    • DOI 10.1016/S0362-546X(01)00281-4, PII S0362546X01002814
    • U. Krause, "Concave Perron-Frobenius theory and applications," Nonlinear Anal., vol. 47, no. 3, pp. 1457-1466, 2001. (Pubitemid 32733039)
    • (2001) Nonlinear Analysis, Theory, Methods and Applications , vol.47 , Issue.3 , pp. 1457-1466
    • Krause, U.1
  • 30
    • 0032648447 scopus 로고    scopus 로고
    • Capacity of a mobile multiple antenna communication link in Rayleigh flat fading
    • T. L. Marzetta and B. M. Hochwald, "Capacity of a mobile multiple antenna communication link in Rayleigh flat fading," IEEE Trans. Inf. Theory, vol. 45, no. 1, pp. 139-157, 1999.
    • (1999) IEEE Trans. Inf. Theory , vol.45 , Issue.1 , pp. 139-157
    • Marzetta, T.L.1    Hochwald, B.M.2
  • 31
    • 0036611984 scopus 로고    scopus 로고
    • Multiple-antennas and isotropically random unitary inputs: The received signal density in closed form
    • DOI 10.1109/TIT.2002.1003835, PII S0018944802040117
    • B. Hassibi and T. L. Marzetta, "Multiple-antenna and isotropically random unitary inputs: The received signal density in closed form," IEEE Trans. Inf. Theory, vol. 48, no. 6, pp. 1473-1484, Jun. 2002. (Pubitemid 34759857)
    • (2002) IEEE Transactions on Information Theory , vol.48 , Issue.6 , pp. 1473-1484
    • Hassibi, B.1    Marzetta, T.L.2
  • 32
    • 23744499731 scopus 로고    scopus 로고
    • A covariance shaping framework for linear multiuser detection
    • DOI 10.1109/TIT.2005.850049
    • Y. C. Eldar and S. Shamai, "A covariance shaping framework for linear multiuser detection," IEEE Trans. Inf. Theory, vol. 51, no. 7, pp. 2426-2446, 2005. (Pubitemid 41136401)
    • (2005) IEEE Transactions on Information Theory , vol.51 , Issue.7 , pp. 2426-2446
    • Eldar, Y.C.1    Shamai, S.2
  • 33
    • 68049121093 scopus 로고    scopus 로고
    • Anomaly detection: A survey
    • Jul
    • V. Chandola, A. Banerjee, and V. Kumar, "Anomaly detection: A survey," ACM Comput. Surv., vol. 41, no. 15, pp. 1-58, Jul. 2009.
    • (2009) ACM Comput. Surv. , vol.41 , Issue.15 , pp. 1-58
    • Chandola, V.1    Banerjee, A.2    Kumar, V.3
  • 35
    • 7044249783 scopus 로고    scopus 로고
    • Angular Gaussian and Cauchy distribution
    • C. Auderset, C. Mazza, and E. A. Ruh, "Angular Gaussian and Cauchy distribution," J. Multivar. Anal., vol. 93, no. 1, pp. 180-197, 2005.
    • (2005) J. Multivar. Anal. , vol.93 , Issue.1 , pp. 180-197
    • Auderset, C.1    Mazza, C.2    Ruh, E.A.3
  • 37
    • 34247990255 scopus 로고
    • On the Kolmogorov-Smirnov test for normality with mean and variance unknown
    • H. W. Lilliefors, "On the Kolmogorov-Smirnov test for normality with mean and variance unknown," J. Amer. Stat. Assoc., vol. 62, pp. 399-402, 1967.
    • (1967) J. Amer. Stat. Assoc. , vol.62 , pp. 399-402
    • Lilliefors, H.W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.