Lognormal Distributions and Geometric Averages of Symmetric Positive Definite Matrices
暂无分享,去创建一个
[1] Roland Bammer,et al. Occipital‐Callosal Pathways in Children: Validation and Atlas Development , 2005, Annals of the New York Academy of Sciences.
[2] P. Basser,et al. Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. 1996. , 1996, Journal of magnetic resonance.
[3] R. Bhattacharya,et al. Statistics on Riemannian manifolds: asymptotic distribution and curvature , 2008 .
[4] Ying Yao,et al. An approximate degrees of freedom solution to the multivariate Behrens-Fisher problem* , 1965 .
[5] Y. Benjamini,et al. Controlling the false discovery rate: a practical and powerful approach to multiple testing , 1995 .
[6] Jonathan E. Taylor,et al. Inference for eigenvalues and eigenvectors of Gaussian symmetric matrices , 2008, 0901.3290.
[7] Paul M. Thompson,et al. Generalized Tensor-Based Morphometry of HIV/AIDS Using Multivariate Statistics on Deformation Tensors , 2008, IEEE Transactions on Medical Imaging.
[8] Tom Leonard,et al. Bayesian Inference for a Covariance Matrix , 1992 .
[9] Xiuwen Liu,et al. Extrinsic analysis on manifolds is computationally faster than intrinsic analysis with applications to quality control by machine vision , 2012 .
[10] Morris Newman,et al. Numerical values of Goldberg’s coefficients in the series for (^{}^{}) , 1987 .
[11] D. Parker,et al. A geometric analysis of diffusion tensor measurements of the human brain , 2000, Magnetic resonance in medicine.
[12] Hongtu Zhu,et al. Intrinsic Regression Models for Positive-Definite Matrices With Applications to Diffusion Tensor Imaging , 2009, Journal of the American Statistical Association.
[13] S. R. Searle,et al. Vec and vech operators for matrices, with some uses in jacobians and multivariate statistics , 1979 .
[14] Karl Goldberg,et al. The formal power series for $\log e^xe^y$ , 1956 .
[15] R. Bhattacharya,et al. LARGE SAMPLE THEORY OF INTRINSIC AND EXTRINSIC SAMPLE MEANS ON MANIFOLDS—II , 2003 .
[16] I. Dryden,et al. Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging , 2009, 0910.1656.
[17] Xavier Pennec,et al. A Riemannian Framework for Tensor Computing , 2005, International Journal of Computer Vision.
[18] Roland Bammer,et al. Diffusion tensor imaging using single‐shot SENSE‐EPI , 2002, Magnetic resonance in medicine.
[19] S.T. Smith,et al. Covariance, subspace, and intrinsic Crame/spl acute/r-Rao bounds , 2005, IEEE Transactions on Signal Processing.
[20] Jimmie D. Lawson,et al. The Geometric Mean, Matrices, Metrics, and More , 2001, Am. Math. Mon..
[21] Tom Leonard,et al. The Matrix-Logarithmic Covariance Model , 1996 .
[22] Paul M. Thompson,et al. Surface-Constrained Volumetric Brain Registration Using Harmonic Mappings , 2007, IEEE Transactions on Medical Imaging.
[23] Ofer Pasternak,et al. The effect of metric selection on the analysis of diffusion tensor MRI data , 2010, NeuroImage.
[24] D. Le Bihan,et al. Diffusion tensor imaging: Concepts and applications , 2001, Journal of magnetic resonance imaging : JMRI.
[25] Maher Moakher,et al. A rigorous framework for diffusion tensor calculus , 2005, Magnetic resonance in medicine.
[26] T. O. Lewis,et al. Quadratic Matrix Equations , 1974 .
[27] Leif Ellingson,et al. Nonparametric two-sample tests on homogeneous Riemannian manifolds, Cholesky decompositions and Diffusion Tensor Image analysis , 2013, J. Multivar. Anal..
[28] Leif Ellingson,et al. Nonparametric bootstrap of sample means of positive-definite matrices with an application to diffusion-tensor-imaging data analysis , 2017, Commun. Stat. Simul. Comput..
[29] José Manuel Corcuera,et al. INTRINSIC ANALYSIS OF STATISTICAL ESTIMATION , 1995 .
[30] R. Dougherty,et al. Group Comparison of Eigenvalues and Eigenvectors of Diffusion Tensors , 2010, Journal of the American Statistical Association.
[31] Maher Moakher,et al. A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices , 2005, SIAM J. Matrix Anal. Appl..
[32] David Groisser. Newton's method, zeroes of vector fields, and the Riemannian center of mass , 2004, Adv. Appl. Math..
[33] Maher Moakher,et al. The Riemannian Geometry of the Space of Positive-Definite Matrices and Its Application to the Regularization of Positive-Definite Matrix-Valued Data , 2011, Journal of Mathematical Imaging and Vision.
[34] N. Ayache,et al. Log‐Euclidean metrics for fast and simple calculus on diffusion tensors , 2006, Magnetic resonance in medicine.
[35] N. Ayache,et al. Clinical DT-MRI Estimation, Smoothing, and Fiber Tracking With Log-Euclidean Metrics , 2007 .
[36] Jan R. Magnus,et al. The Elimination Matrix: Some Lemmas and Applications , 1980, SIAM J. Algebraic Discret. Methods.
[37] J. M. Oller,et al. AN EXPLICIT SOLUTION OF INFORMATION GEODESIC EQUATIONS FOR THE MULTIVARIATE NORMAL MODEL , 1991 .
[38] P. Thomas Fletcher,et al. Riemannian geometry for the statistical analysis of diffusion tensor data , 2007, Signal Process..
[39] Yongdo Lim,et al. Weighted means and Karcher equations of positive operators , 2013, Proceedings of the National Academy of Sciences.
[40] A. Terras. Asymptotics of special functions and the central limit theorem on the space n of positive n × n matrices , 1987 .
[41] Rachid Deriche,et al. Statistics on the Manifold of Multivariate Normal Distributions: Theory and Application to Diffusion Tensor MRI Processing , 2006, Journal of Mathematical Imaging and Vision.
[42] M. Fréchet. Les éléments aléatoires de nature quelconque dans un espace distancié , 1948 .
[43] J. Ashburner,et al. Nonlinear spatial normalization using basis functions , 1999, Human brain mapping.
[44] S. Cowin,et al. Six-dimensional orthogonal tensorrepresentation of the rotation about an axis in three dimensions , 1995 .
[45] L. Skovgaard. A Riemannian geometry of the multivariate normal model , 1984 .
[46] Brian A Wandell,et al. Temporal-callosal pathway diffusivity predicts phonological skills in children , 2007, Proceedings of the National Academy of Sciences.
[47] R. Bhatia,et al. Riemannian geometry and matrix geometric means , 2006 .
[48] Nicholas Ayache,et al. Geometric Means in a Novel Vector Space Structure on Symmetric Positive-Definite Matrices , 2007, SIAM J. Matrix Anal. Appl..
[49] Brandon Whitcher,et al. Statistical group comparison of diffusion tensors via multivariate hypothesis testing , 2007, Magnetic resonance in medicine.
[50] Xavier Pennec,et al. Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements , 2006, Journal of Mathematical Imaging and Vision.
[51] Morris Newman,et al. Numerical values of Goldberg’s coefficients in the series for (^{}^{}) , 1987 .