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Volumn 35, Issue 1, 1999, Pages 113-137

Dual differential geometry associated with the Kullbaek-Leibler information on the Gaussian distributions and its 2-parameter deformations

Author keywords

( , ) divergence; Dual affine connections; Dunford taylor integral; Kullback leibler information; Legendre transformation; Matrix convex function; Matrix differential

Indexed keywords


EID: 0038257744     PISSN: 09165746     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (35)

References (16)
  • 1
    • 0010951451 scopus 로고
    • Maximum-Likelihood estimation of the parameters of a multivariate normal distribution
    • T.W. Anderson and I. Olkin, Maximum-Likelihood estimation of the parameters of a multivariate normal distribution, Linear Algebra and Its Applications, 70, 141-171 (1985).
    • (1985) Linear Algebra and Its Applications , vol.70 , pp. 141-171
    • Anderson, T.W.1    Olkin, I.2
  • 2
    • 0003355631 scopus 로고
    • Differential geometrical method in statistics
    • Springer Verlag, Berlin
    • S. Amari, Differential geometrical method in statistics, Lec. Notes in Statist. Vol.28, Springer Verlag, Berlin (1985).
    • (1985) Lec. Notes in Statist , vol.28
    • Amari, S.1
  • 5
    • 0001476546 scopus 로고
    • Exponential models with affine dual foliations
    • O.E. Barndorff-Nielsen and P. Blaesild, Exponential models with affine dual foliations, Ann.Statist. 11, 735-769 (1983).
    • (1983) Ann.Statist , vol.11 , pp. 735-769
    • Barndorff-Nielsen, O.E.1    Blaesild, P.2
  • 6
    • 0000057533 scopus 로고
    • Improper affine hyperspheres of convex type and a generalization of a theorem by K.Jörgens
    • E. Calabi, Improper affine hyperspheres of convex type and a generalization of a theorem by K.Jörgens, Michigan Math.J., Vol.5, 105-126 (1958).
    • (1958) Michigan Math.J , vol.5 , pp. 105-126
    • Calabi, E.1
  • 7
    • 0000924020 scopus 로고
    • On the regularity of the monge-ampere equation
    • C. Chen and S. Yau, On the regularity of the Monge-Ampere equation, Comm.Pure Appl.Math. Vol XXX, 41-68 (1977).
    • (1977) Comm.Pure Appl.Math , vol.xxx , pp. 41-68
    • Chen, C.1    Yau, S.2
  • 8
    • 0000551847 scopus 로고
    • Defining the curvature of a statistical problem (with Discussion)
    • B. Efron, Defining the curvature of a statistical problem (with Discussion), Ann. Statist. 6, 1189-1242 (1975).
    • (1975) Ann. Statist , vol.6 , pp. 1189-1242
    • Efron, B.1
  • 9
    • 0000767211 scopus 로고
    • Gradient systems in view of information geometry
    • A. Fujiwara and S. Amari, Gradient systems in view of information geometry, Physica D80, No.3, 317-327 (1995).
    • (1995) Physica , vol.D80 , Issue.3 , pp. 317-327
    • Fujiwara, A.1    Amari, S.2
  • 11
    • 36649022319 scopus 로고
    • Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture
    • E.H. Lieb, Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture, Advances in Mathematics, 11, 267-288 (1973).
    • (1973) Advances in Mathematics , vol.11 , pp. 267-288
    • Lieb, E.H.1
  • 12
    • 0000684487 scopus 로고
    • The informatiton matrix,skewness tensor and a-connections for the general multivariate elliptic distribution
    • A.F.S. Mitchell, The informatiton matrix,skewness tensor and a-connections for the general multivariate elliptic distribution, Ann.Inst.Statist.Math. Vol.41, No.2, 289-304 (1989).
    • (1989) Ann.Inst.Statist.Math , vol.41 , Issue.2 , pp. 289-304
    • Mitchell, A.F.S.1
  • 13
    • 0030508084 scopus 로고    scopus 로고
    • Dualistic Differential Geometry of Positive Definite Matrices and Its Applications to Related Problems
    • A. Ohara, N. Suda and S. Amari, Dualistic Differential Geometry of Positive Definite Matrices and Its Applications to Related Problems, Linear Algebra and Its Applications, 247, 31-53 (1996).
    • (1996) Linear Algebra and Its Applications , vol.247 , pp. 31-53
    • Ohara, A.1    Suda, N.2    Amari, S.3
  • 14
    • 0003626674 scopus 로고    scopus 로고
    • Matrix Algebra and Its Applications to Statistics and Econometrics
    • C.R. Rao and M.B. Rao, Matrix Algebra and Its Applications to Statistics and Econometrics, World Scientific (1998).
    • (1998) World Scientific
    • Rao, C.R.1    Rao, M.B.2
  • 15
    • 84972580865 scopus 로고
    • Hessian manifolds of constant Hessian sectional curvature
    • H. Shima, Hessian manifolds of constant Hessian sectional curvature, J.Math.Soc.Japan. Vol.47, No.4, 735-753 (1995).
    • (1995) J.Math.Soc.Japan , vol.47 , Issue.4 , pp. 735-753
    • Shima, H.1
  • 16
    • 0037582222 scopus 로고
    • A Riemannian geometry of the multivariate normal model
    • L.T. Skovgaard, A Riemannian geometry of the multivariate normal model, Scand.J.Statist., 11, 211-223 (1984).
    • (1984) Scand.J.Statist , vol.11 , pp. 211-223
    • Skovgaard, L.T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.