Properties and applications of Fisher distribution on the rotation group

DOI10.1016/j.jmva.2013.01.010zbMath1283.60011arXiv1110.0721OpenAlexW2110947887MaRDI QIDQ391572

Akimichi Takemura, Katsuyoshi Ohara, Hiroki Shibata, Tomonari Sei, Nobuki Takayama

Publication date: 10 January 2014

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.0721

zbMATH Keywords

maximum likelihood estimationrotation groupdirectional statisticsalgebraic statisticsholonomic gradient descent

Mathematics Subject Classification ID

Directional data; spatial statistics (62H11) Point estimation (62F10) Probability distributions: general theory (60E05) Methods of reduced gradient type (90C52) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items (12)

Algebraic analysis of rotation data ⋮ The holonomic gradient method for the distribution function of the largest root of a Wishart matrix ⋮ Nonlinear algebra and applications ⋮ On the exact maximum likelihood inference of Fisher-Bingham distributions using an adjusted holonomic gradient method ⋮ Conjugate priors and posterior inference for the matrix Langevin distribution on the Stiefel manifold ⋮ Holonomic gradient descent for the Fisher-Bingham distribution on the \(d\)-dimensional sphere ⋮ Algebraic analysis of the hypergeometric function \(_1F_1\) of a matrix argument ⋮ Calculating the normalising constant of the Bingham distribution on the sphere using the holonomic gradient method ⋮ Estimation of exponential-polynomial distribution by holonomic gradient descent ⋮ THE ANNIHILATING IDEAL OF THE FISHER INTEGRAL ⋮ Density estimation for mixed Euclidean and non-Euclidean data in the presence of measurement error ⋮ Nonparametric regression on Lie groups with measurement errors

Uses Software

• Macaulay2
• Risa/Asir
• hgm R

Cites Work

• The holonomic gradient method for the distribution function of the largest root of a Wishart matrix
• Holonomic gradient descent and its application to the Fisher-Bingham integral
• Exponential models for directional data
• Maximum likelihood estimators for the matrix von Mises-Fisher and Bingham distributions
• Information and Exponential Families
• ESTIMATION OF THE CONCENTRATION PARAMETERS OF THE FISHER MATRIX DISTRIBUTION ON 50(3) AND THE BINGHAM DISTRIBUTION ON S_q, q≥ 2
• Procrustes analysis on some special manifolds
• Using Algebraic Geometry
• Saddlepoint approximations for the Bingham and Fisher–Bingham normalising constants
• Calculation of Zonal Polynomial Coefficients by Use of the Laplace-Beltrami Operator
• Systems of Partial Differential Equations for Hypergeometric Functions of Matrix Argument
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