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Volumn 56, Issue 6, 2008, Pages 2194-2205

Linear regression with Gaussian model uncertainty: Algorithms and bounds

Author keywords

Errors in variables (EIV); Linear models; Maximum likelihood (ML) estimation; Random model matrix; Total least squares

Indexed keywords

LINEAR REGRESSION; MATHEMATICAL MODELS; MATRIX ALGEBRA; MAXIMUM LIKELIHOOD ESTIMATION; RANDOM PROCESSES; UNCERTAINTY ANALYSIS;

EID: 44849089298     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2007.914323     Document Type: Article
Times cited : (67)

References (33)
  • 5
    • 11844289605 scopus 로고    scopus 로고
    • Robust mean-squared error estimation in the presence of model uncertainties
    • Jan
    • Y. C. Eldar, A. Ben-Tal, and A. Nemirovski, "Robust mean-squared error estimation in the presence of model uncertainties," IEEE Trans. Signal Process., vol. 53, no. 1, pp. 168-181, Jan. 2005.
    • (2005) IEEE Trans. Signal Process , vol.53 , Issue.1 , pp. 168-181
    • Eldar, Y.C.1    Ben-Tal, A.2    Nemirovski, A.3
  • 6
    • 41849084092 scopus 로고    scopus 로고
    • Blind minimax estimation
    • Sep
    • Z. B. Haim and Y. C. Eldar, "Blind minimax estimation," IEEE Trans. Inf. Theory, vol. 53, no. 9, pp. 3145-3157, Sep. 2007.
    • (2007) IEEE Trans. Inf. Theory , vol.53 , Issue.9 , pp. 3145-3157
    • Haim, Z.B.1    Eldar, Y.C.2
  • 7
    • 0031536271 scopus 로고    scopus 로고
    • Robust solutions to least-squares problems with uncertain data
    • Oct
    • L. E. Ghaoui and H. Lebret, "Robust solutions to least-squares problems with uncertain data," SIAM J. Matrix Anal. Appl., pp. 1034-1064, Oct. 1997.
    • (1997) SIAM J. Matrix Anal. Appl , pp. 1034-1064
    • Ghaoui, L.E.1    Lebret, H.2
  • 8
    • 0032340223 scopus 로고    scopus 로고
    • Parameter estimation in the presence of bounded data uncertainties
    • Jan
    • S. Chandrasekaran, M. G. G. H. Golub, and A. H. Sayed, "Parameter estimation in the presence of bounded data uncertainties," SIAM J. Matrix Anal. Appl., pp. 235-252, Jan. 1998.
    • (1998) SIAM J. Matrix Anal. Appl , pp. 235-252
    • Chandrasekaran, S.1    Golub, M.G.G.H.2    Sayed, A.H.3
  • 9
    • 33645836731 scopus 로고    scopus 로고
    • Maximum likelihood estimation in linear models with a Gaussian model matrix
    • May
    • A.Wiesel, Y. C. Eldar, and A. Beck, "Maximum likelihood estimation in linear models with a Gaussian model matrix," IEEE Signal Process. Lett., vol. 13, no. 5, pp. 292-295, May 2006.
    • (2006) IEEE Signal Process. Lett , vol.13 , Issue.5 , pp. 292-295
    • Wiesel, A.1    Eldar, Y.C.2    Beck, A.3
  • 10
    • 84881348920 scopus 로고    scopus 로고
    • 2, l ∞ uncertain linear approximation problems using convex optimization, in Proc. Amer. Control Conf., Jun. 1998, 6 pp. 3487-3491.
    • 2, l ∞ uncertain linear approximation problems using convex optimization, " in Proc. Amer. Control Conf., Jun. 1998, vol. 6 pp. 3487-3491.
  • 11
    • 31344457502 scopus 로고    scopus 로고
    • Minimax estimation of deterministic parameters in linear models with a random model matrix
    • Feb
    • Y. C. Eldar, "Minimax estimation of deterministic parameters in linear models with a random model matrix," IEEE Trans. Signal Process., vol. 45, no. 2, pp. 601-612, Feb. 2006.
    • (2006) IEEE Trans. Signal Process , vol.45 , Issue.2 , pp. 601-612
    • Eldar, Y.C.1
  • 13
    • 0003297912 scopus 로고
    • The total least squares problem: Computational aspects and analysis
    • Philadelphia, PA: SIAM
    • S. V. Huffel and J. Vandewalle, "The total least squares problem: Computational aspects and analysis," in Frontiers in Applied Mathematics 9. Philadelphia, PA: SIAM, 1991.
    • (1991) Frontiers in Applied Mathematics 9
    • Huffel, S.V.1    Vandewalle, J.2
  • 14
  • 15
    • 0035362079 scopus 로고    scopus 로고
    • Iterative maximum-likelihood sequence estimation for space-time coded systems
    • Jun
    • Y. Li, C. N. Georghiades, and G. Huang, "Iterative maximum-likelihood sequence estimation for space-time coded systems," IEEE Trans. Commun., vol. 49, no. 6, pp. 948-951, Jun. 2001.
    • (2001) IEEE Trans. Commun , vol.49 , Issue.6 , pp. 948-951
    • Li, Y.1    Georghiades, C.N.2    Huang, G.3
  • 16
    • 11844280356 scopus 로고    scopus 로고
    • Iterative EM receiver for space-time coded systems in MIMO frequency-selective fading channels with channel gain and order estimation
    • Nov
    • D. K. C. So and R. S. Cheng, "Iterative EM receiver for space-time coded systems in MIMO frequency-selective fading channels with channel gain and order estimation," IEEE Trans. Wireless Commun., vol. 3, no. 6, pp. 1928-1935, Nov. 2004.
    • (2004) IEEE Trans. Wireless Commun , vol.3 , Issue.6 , pp. 1928-1935
    • So, D.K.C.1    Cheng, R.S.2
  • 17
    • 85032751764 scopus 로고    scopus 로고
    • On nonexistence of the maximum likelihood estimate in blind multichannel identification
    • Jul
    • P. Stoica and J. Li, "On nonexistence of the maximum likelihood estimate in blind multichannel identification," IEEE Signal Process. Mag., vol. 22, no. 4, pp. 99-101, Jul. 2005.
    • (2005) IEEE Signal Process. Mag , vol.22 , Issue.4 , pp. 99-101
    • Stoica, P.1    Li, J.2
  • 19
    • 33645823790 scopus 로고    scopus 로고
    • Hidden convexity based near maximum-likelihood CDMA detection
    • presented at the, Baltimore, MD, Mar. 16-18
    • Y. C. Eldar and A. Beck, "Hidden convexity based near maximum-likelihood CDMA detection," presented at the 39th Annu. Conf. Inf. Sci. Syst., Baltimore, MD, Mar. 16-18, 2005.
    • (2005) 39th Annu. Conf. Inf. Sci. Syst
    • Eldar, Y.C.1    Beck, A.2
  • 20
    • 84972513554 scopus 로고
    • On general minimax theorems
    • M. Sion, "On general minimax theorems," Pac. J. Math., vol. 8, pp. 171-176, 1958.
    • (1958) Pac. J. Math , vol.8 , pp. 171-176
    • Sion, M.1
  • 22
    • 33847101829 scopus 로고    scopus 로고
    • On the solution of the Tikhonov regularization of the total least squares
    • A. Beck and A. Ben-Tal, "On the solution of the Tikhonov regularization of the total least squares," SIAM J. Optim., vol. 17, no. 1, pp. 98-118.
    • SIAM J. Optim , vol.17 , Issue.1 , pp. 98-118
    • Beck, A.1    Ben-Tal, A.2
  • 23
    • 34247386378 scopus 로고    scopus 로고
    • Finding a global optimal solution for a quadratically constrained fractional quadratic problem with applications to the regularized total least squares
    • A. Beck, A. Ben-Tal, and M. Teboulle, "Finding a global optimal solution for a quadratically constrained fractional quadratic problem with applications to the regularized total least squares," SIAM J. Matrix Anal. Appl., vol. 28, no. 2, pp. 425-445, 2006.
    • (2006) SIAM J. Matrix Anal. Appl , vol.28 , Issue.2 , pp. 425-445
    • Beck, A.1    Ben-Tal, A.2    Teboulle, M.3
  • 24
    • 0034506768 scopus 로고    scopus 로고
    • The joint MAP-ML and its relation to ML and to extended least-squares
    • Dec
    • A. Yeredor, "The joint MAP-ML and its relation to ML and to extended least-squares," IEEE Trans. Signal Process., vol. 48, no. 12, pp. 3484-3492, Dec. 2000.
    • (2000) IEEE Trans. Signal Process , vol.48 , Issue.12 , pp. 3484-3492
    • Yeredor, A.1
  • 25
    • 33947622149 scopus 로고    scopus 로고
    • Maximum likelihood estimation in random linear models: Generalizations and performance analysis
    • Toulouse, France, May
    • A. Wiesel and Y. C. Eldar, "Maximum likelihood estimation in random linear models: Generalizations and performance analysis," in Proc. IEEE Int. Conf. Acoust. Speech Signal Process., Toulouse, France, May 2006, vol. 5, pp. 993-996.
    • (2006) Proc. IEEE Int. Conf. Acoust. Speech Signal Process , vol.5 , pp. 993-996
    • Wiesel, A.1    Eldar, Y.C.2
  • 26
    • 0031696439 scopus 로고    scopus 로고
    • The modified Cramer-Rao bound in vector parameter estimation
    • Jan
    • F. Gini, R. Reggiannini, and U. Mengali, "The modified Cramer-Rao bound in vector parameter estimation," IEEE Trans. Commun., vol. 46, no. 1, pp. 2120-2127, Jan. 1998.
    • (1998) IEEE Trans. Commun , vol.46 , Issue.1 , pp. 2120-2127
    • Gini, F.1    Reggiannini, R.2    Mengali, U.3
  • 27
    • 0017972132 scopus 로고
    • A modified Cramer-Rao bound and its applications
    • May
    • R. Miller and C. Chang, "A modified Cramer-Rao bound and its applications," IEEE Trans. Inf. Theory, vol. IT-24, no. 3, pp. 398-400, May 1978.
    • (1978) IEEE Trans. Inf. Theory , vol.IT-24 , Issue.3 , pp. 398-400
    • Miller, R.1    Chang, C.2
  • 28
    • 0031139326 scopus 로고    scopus 로고
    • A Barankin-type lower bound on the estimation error of a hybrid parameter vector
    • May
    • I. Reuven and H. Messer, "A Barankin-type lower bound on the estimation error of a hybrid parameter vector," IEEE Trans. Inf. Theory, vol. 43, no. 3, pp. 1084-1093, May 1997.
    • (1997) IEEE Trans. Inf. Theory , vol.43 , Issue.3 , pp. 1084-1093
    • Reuven, I.1    Messer, H.2
  • 29
    • 0034486691 scopus 로고    scopus 로고
    • On the use of Cramer-Rao like bounds in the presence of random nuisance parameters
    • Dec
    • F. Gini and R. Reggiannini, "On the use of Cramer-Rao like bounds in the presence of random nuisance parameters," IEEE Trans. Commun., vol. 48, no. 12, pp. 2120-2127, Dec. 2000.
    • (2000) IEEE Trans. Commun , vol.48 , Issue.12 , pp. 2120-2127
    • Gini, F.1    Reggiannini, R.2
  • 30
    • 0001756412 scopus 로고
    • Estimation of a system pulse transfer function in the presence of noise
    • Jul
    • M. J. Levin, "Estimation of a system pulse transfer function in the presence of noise," IEEE Trans. Autom. Control, vol. AC-9, no. 3, pp. 229-235, Jul. 1964.
    • (1964) IEEE Trans. Autom. Control , vol.AC-9 , Issue.3 , pp. 229-235
    • Levin, M.J.1
  • 31
    • 33947415699 scopus 로고    scopus 로고
    • A new approach to variable selection using the TLS approach
    • Jan
    • J. J. Fuchs and S. Maria, "A new approach to variable selection using the TLS approach," IEEE Trans. Signal Process., vol. 55, no. 1, pp. 10-19, Jan. 2007.
    • (2007) IEEE Trans. Signal Process , vol.55 , Issue.1 , pp. 10-19
    • Fuchs, J.J.1    Maria, S.2
  • 32
    • 0001294645 scopus 로고
    • The fitting of straight lines if both variables are subject to error
    • Sep
    • A. Wald, "The fitting of straight lines if both variables are subject to error," Ann. Math. Statist., vol. 11, no. 3, pp. 284-300, Sep. 1940.
    • (1940) Ann. Math. Statist , vol.11 , Issue.3 , pp. 284-300
    • Wald, A.1
  • 33
    • 0030215043 scopus 로고    scopus 로고
    • Exploring estimator bias-variance tradeoffs using the uniform CR bound
    • Aug
    • A. O. Hero, J. A. Fessler, and M. Usman, "Exploring estimator bias-variance tradeoffs using the uniform CR bound," IEEE Trans. Signal Process., vol. 44, no. 8, pp. 2026-2041, Aug. 1996.
    • (1996) IEEE Trans. Signal Process , vol.44 , Issue.8 , pp. 2026-2041
    • Hero, A.O.1    Fessler, J.A.2    Usman, M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.