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Lognormal Distributions and Geometric Averages of Symmetric Positive Definite Matrices

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  • Armin Schwartzman

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  • Armin Schwartzman, 2016. "Lognormal Distributions and Geometric Averages of Symmetric Positive Definite Matrices," International Statistical Review, International Statistical Institute, vol. 84(3), pages 456-486, December.
    • Handle: RePEc:bla:istatr:v:84:y:2016:i:3:p:456-486
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    File URL: http://hdl.handle.net/10.1111/insr.12113
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    References listed on IDEAS

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    1. Magnus, J.R. & Neudecker, H., 1980. "The elimination matrix : Some lemmas and applications," Other publications TiSEM 0e3315d3-846c-4bc5-928e-f, Tilburg University, School of Economics and Management.
    2. Terras, Audrey, 1987. "Asymptotics of special functions and the central limit theorem on the space [Weierstrass p]n of positive n - n matrices," Journal of Multivariate Analysis, Elsevier, vol. 23(1), pages 13-36, October.
    3. Schwartzman, Armin & Dougherty, Robert F. & Taylor, Jonathan E., 2010. "Group Comparison of Eigenvalues and Eigenvectors of Diffusion Tensors," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 588-599.
    4. Osborne, Daniel & Patrangenaru, Vic & Ellingson, Leif & Groisser, David & Schwartzman, Armin, 2013. "Nonparametric two-sample tests on homogeneous Riemannian manifolds, Cholesky decompositions and Diffusion Tensor Image analysis," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 163-175.
    5. Zhu, Hongtu & Chen, Yasheng & Ibrahim, Joseph G. & Li, Yimei & Hall, Colin & Lin, Weili, 2009. "Intrinsic Regression Models for Positive-Definite Matrices With Applications to Diffusion Tensor Imaging," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1203-1212.
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    Cited by:

    1. Zhou Lan & Brian J. Reich & Joseph Guinness & Dipankar Bandyopadhyay & Liangsuo Ma & F. Gerard Moeller, 2022. "Geostatistical modeling of positive‐definite matrices: An application to diffusion tensor imaging," Biometrics, The International Biometric Society, vol. 78(2), pages 548-559, June.
    2. Benoit Ahanda & Daniel E. Osborne & Leif Ellingson, 2022. "Robustness of lognormal confidence regions for means of symmetric positive definite matrices when applied to mixtures of lognormal distributions," METRON, Springer;Sapienza Università di Roma, vol. 80(3), pages 281-303, December.

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