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Volumn 296, Issue 1-3, 1999, Pages 171-181

A matrix version of the Wielandt inequality and its applications to statistics

Author keywords

Canonical correlation; Cauchy Schwarz inequality; Condition number; Generalized inverse; Kantorovich inequality; Wielandt inequality

Indexed keywords


EID: 0033464626     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(99)00117-2     Document Type: Article
Times cited : (29)

References (20)
  • 1
    • 0000355804 scopus 로고
    • The Gauss-Markov theorem for regression models with possibly singular covariances
    • A. Albert, The Gauss-Markov theorem for regression models with possibly singular covariances, SIAM J. Appl. Math. 24 (1973) 182-187.
    • (1973) SIAM J. Appl. Math. , vol.24 , pp. 182-187
    • Albert, A.1
  • 2
    • 0000748103 scopus 로고
    • Generalized matrix versions of the Cauchy-Schwarz and Kantorovich inequalities
    • J.K. Baksalary, S. Puntanen, Generalized matrix versions of the Cauchy-Schwarz and Kantorovich inequalities, Aequationes Math. 41 (1991) 103-110.
    • (1991) Aequationes Math. , vol.41 , pp. 103-110
    • Baksalary, J.K.1    Puntanen, S.2
  • 3
    • 0042970119 scopus 로고
    • A property of the dispersion matrix of the best linear unbaised estimator in the general Gauss-Markov model
    • J.K. Baksalary, S. Puntanen, G.P.H. Styan, A property of the dispersion matrix of the best linear unbaised estimator in the general Gauss-Markov model, Sankhya A 52 (1990) 279-296.
    • (1990) Sankhya A , vol.52 , pp. 279-296
    • Baksalary, J.K.1    Puntanen, S.2    Styan, G.P.H.3
  • 4
    • 0041467212 scopus 로고
    • Some inequalities involving the Euclidean condition of a matrix
    • F.L. Bauer, A.S. Householder, Some inequalities involving the Euclidean condition of a matrix, Numerische Mathematik 2 (1960) 308-311.
    • (1960) Numerische Mathematik , vol.2 , pp. 308-311
    • Bauer, F.L.1    Householder, A.S.2
  • 5
    • 0012488872 scopus 로고
    • A maximization problem and its applications to canonical correlation
    • M.L. Eaton, A maximization problem and its applications to canonical correlation, J. Multivariate Anal. 6 (1976) 422-425.
    • (1976) J. Multivariate Anal. , vol.6 , pp. 422-425
    • Eaton, M.L.1
  • 6
    • 0002204016 scopus 로고
    • Determination of the inertia of a partitioned Hermitian matrix
    • E.V. Haynsworth, Determination of the inertia of a partitioned Hermitian matrix, Linear Algebra Appl. 1 (1968) 73-81.
    • (1968) Linear Algebra Appl. , vol.1 , pp. 73-81
    • Haynsworth, E.V.1
  • 8
    • 0000107975 scopus 로고
    • Relations between two sets of variates
    • H. Hottelling, Relations between two sets of variates, Biometrika 28 (1936) 321-377.
    • (1936) Biometrika , vol.28 , pp. 321-377
    • Hottelling, H.1
  • 9
    • 0003757202 scopus 로고
    • Reprint Edition, Dover, New York, Original Version: Blaisdell, New York
    • A.S. Householder, The Theory of Matrices in Numerical Analysis, Reprint Edition, Dover, New York, pp. 81-85. Original Version: Blaisdell, New York, 1964.
    • (1964) The Theory of Matrices in Numerical Analysis , pp. 81-85
    • Householder, A.S.1
  • 10
    • 0002056449 scopus 로고
    • Matrix version of the Cauchy and Kantorovich inequalities
    • A.W. Marshall, I. Olkin, Matrix version of the Cauchy and Kantorovich inequalities, Aequationes Math. 40 (1990) 89-93.
    • (1990) Aequationes Math. , vol.40 , pp. 89-93
    • Marshall, A.W.1    Olkin, I.2
  • 11
    • 0010992234 scopus 로고
    • Matrix versions of some means inequalities
    • B. Mond, J.E. Pecaric, Matrix versions of some means inequalities, Aust. Math. Soc. Gaz. 20 (1993) 117-120.
    • (1993) Aust. Math. Soc. Gaz. , vol.20 , pp. 117-120
    • Mond, B.1    Pecaric, J.E.2
  • 14
    • 27344451855 scopus 로고    scopus 로고
    • Some further matrix extensions of the Cauchy-Schwarz and Kantorovich inequalities, with some statistical applications
    • J.E. Pecaric, S. Puntanen, G.P.H. Styan, Some further matrix extensions of the Cauchy-Schwarz and Kantorovich inequalities, with some statistical applications, Linear Algebra Appl. 237 (1996) 455-476.
    • (1996) Linear Algebra Appl. , vol.237 , pp. 455-476
    • Pecaric, J.E.1    Puntanen, S.2    Styan, G.P.H.3
  • 15
    • 0000544111 scopus 로고
    • Least square theory using an estimated dispersion matrix and its applications to measurement of signal
    • L. Lecam, Neyman (Eds.)
    • C.R. Rao, Least square theory using an estimated dispersion matrix and its applications to measurement of signal, in: L. Lecam, Neyman (Eds.), Proceeding of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, 1967, pp. 355-372.
    • (1967) Proceeding of the Fifth Berkeley Symposium on Mathematical Statistics and Probability , vol.1 , pp. 355-372
    • Rao, C.R.1
  • 18
    • 0041968363 scopus 로고
    • A new estimator of regression coefficients in seemingly unrelated regression system
    • S.G. Wang, A new estimator of regression coefficients in seemingly unrelated regression system, Science in China A10 (1988) 1033-1040.
    • (1988) Science in China , vol.A10 , pp. 1033-1040
    • Wang, S.G.1
  • 20
    • 0042468943 scopus 로고
    • Pitman optimalities of covariance improved estimators
    • S.G. Wang, Z.H. Yang, Pitman optimalities of covariance improved estimators, Chinese Sci. Bull. 40 (1995) 12-15.
    • (1995) Chinese Sci. Bull. , vol.40 , pp. 12-15
    • Wang, S.G.1    Yang, Z.H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.