메뉴 건너뛰기




Volumn 321, Issue 1-3, 2000, Pages 307-320

Statistical proofs of some matrix inequalities

Author keywords

15A45; 62B10; 62G05; Carlen's inequality; Cauchy Schwarz inequality; Generalized inverse; Harmonic mean inequality; Information inequalities; Kronecker product; Miline's inequality; Parallel sum of matrices; Schur complement; Schur product

Indexed keywords


EID: 0034365314     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(99)00276-1     Document Type: Article
Times cited : (18)

References (22)
  • 1
    • 0014476598 scopus 로고
    • Conditions for positive and nonnegative definiteness in terms of pseudo inverses
    • Alber A. Conditions for positive and nonnegative definiteness in terms of pseudo inverses. SIAM J. Appl. Math. 17:1969;434-440.
    • (1969) SIAM J. Appl. Math. , vol.17 , pp. 434-440
    • Alber, A.1
  • 2
    • 0001079995 scopus 로고
    • Concavity of certain maps on positive definite matrices and application to Hadamard products
    • Ando T. Concavity of certain maps on positive definite matrices and application to Hadamard products. Linear Algebra Appl. 26:1979;203-241.
    • (1979) Linear Algebra Appl. , vol.26 , pp. 203-241
    • Ando, T.1
  • 4
    • 0000273265 scopus 로고
    • Superadditivity of Fisher's information and logarithmic Sobolev inequalities
    • Carlen E.A. Superadditivity of Fisher's information and logarithmic Sobolev inequalities. J. Funct. Anal. 101:1991;194-211.
    • (1991) J. Funct. Anal. , vol.101 , pp. 194-211
    • Carlen, E.A.1
  • 6
    • 0010181103 scopus 로고
    • Uber eine ungleichung für positiv definite matrizen
    • Fiedler M. Uber eine ungleichung für positiv definite matrizen. Math. Nachr. 23:1961;197-199.
    • (1961) Math. Nachr. , vol.23 , pp. 197-199
    • Fiedler, M.1
  • 7
    • 0031091907 scopus 로고    scopus 로고
    • Statistical meaning of Carlen's superadditivity of Fisher information
    • Kagan A., Landsman Z. Statistical meaning of Carlen's superadditivity of Fisher information. Statist. Probab. Lett. 32:1997;175-179.
    • (1997) Statist. Probab. Lett. , vol.32 , pp. 175-179
    • Kagan, A.1    Landsman, Z.2
  • 12
  • 13
    • 0347884294 scopus 로고
    • Statistical proofs of some propositions on nonnegative definite matrices
    • Mitra S.K. Statistical proofs of some propositions on nonnegative definite matrices. Bull. Inter. Statist. Inst. XLV:1973;206-211.
    • (1973) Bull. Inter. Statist. Inst. , vol.45 , pp. 206-211
    • Mitra, S.K.1
  • 14
    • 0346623892 scopus 로고
    • Transformations of the range space and direct orthogonal projector
    • in: J.K. Ghosh et al. (Eds.), Wiley Eastern, New Delhi
    • S.K. Mitra, Transformations of the range space and direct orthogonal projector, in: J.K. Ghosh et al. (Eds.), Statistics and Probability: A Raghu Raj Bahadur Festschrift, Wiley Eastern, New Delhi, 1993, pp. 463-474.
    • (1993) Statistics and Probability: A Raghu Raj Bahadur Festschrift , pp. 463-474
    • Mitra, S.K.1
  • 16
    • 0001185544 scopus 로고
    • A multivariate Tchebycheff's inequality
    • Olkin I., Pratt J. A multivariate Tchebycheff's inequality. Ann. Math. Stat. 29:1958;226-234.
    • (1958) Ann. Math. Stat. , vol.29 , pp. 226-234
    • Olkin, I.1    Pratt, J.2
  • 17
    • 0347884296 scopus 로고    scopus 로고
    • An inequality for the expectation of harmonic mean of random matrices
    • Indian Statistical Institute, Delhi
    • B.L.S. Prakasa Rao, An inequality for the expectation of harmonic mean of random matrices, Technical Report, Indian Statistical Institute, Delhi, 1998.
    • (1998) Technical Report
    • Prakasa Rao, B.L.S.1
  • 19
    • 0039048571 scopus 로고
    • R.A. Fisher: The founder of modern statistics
    • Rao C.R. R.A. Fisher: The founder of modern statistics. Statist. Sci. 7:1992;34-48.
    • (1992) Statist. Sci. , vol.7 , pp. 34-48
    • Rao, C.R.1
  • 20
    • 0347253805 scopus 로고    scopus 로고
    • Seven inequalities in statistical estimation theory
    • Rao C.R. Seven inequalities in statistical estimation theory. Student. 1:1996;149-158.
    • (1996) Student , vol.1 , pp. 149-158
    • Rao, C.R.1
  • 22
    • 33748313606 scopus 로고    scopus 로고
    • Some inequalities on principal submatirces of positive semidefinite matrices
    • Nova South Eastern University, Fort Lauderdale
    • F. Zhang, Some inequalities on principal submatirces of positive semidefinite matrices, Technical Report, Nova South Eastern University, Fort Lauderdale, 1998.
    • (1998) Technical Report
    • Zhang, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.