Approximating the matrix Fisher and Bingham distributions: Applications to spherical regression and procrustes analysis

Anderson, 1970, An asymptotic expansion for the noncentral Wishart distribution, Ann. Math. Statist., 41, 1700, 10.1214/aoms/1177696814 Barndorff-Nielsen, 1982, Exponential transformation models, 379, 41 Bingham, 1974, An antipodally symmetric distribution on the sphere, Ann. Statist., 2, 1201, 10.1214/aos/1176342874 Bingham, 1977 Bingham, 1989 Chang, 1986, Spherical regression, Ann. Statist., 14, 907, 10.1214/aos/1176350041 Chang, 1991, Spherical regression and the statistics of tectonic plate reconstructions, Internat. Statist. Rev. Goodall, 1991, Procrustes methods in the statistical analysis of shape, J. Roy. Statist. Soc. Ser. B, 53, 285 Gower, 1975, Generalized Procrustes analysis, Psychometrika, 40, 33, 10.1007/BF02291478 Gross, 1991, Hypergeometric functions on complex matrix space, Bull. Amer. Math. Soc. (N.S.), 24, 349, 10.1090/S0273-0979-1991-16031-3 Hanna, 1990, On graphically representing the confidence region for an unknown rotation in three dimensions, Comput. & Geosc., 16, 163, 10.1016/0098-3004(90)90127-F James, 1964, Distributions of matrix variates and latent roots derived from normal samples, Ann. Math. Statist., 35, 475, 10.1214/aoms/1177703550 Kent, 1987, Asymptotic expansions for the Bingham distribution, Appl. Statist., 36, 139, 10.2307/2347545 Kent, 1990, The complex Bingham distribution and shape distributions Khatri, 1977, The von Mises-Fisher matrix distribution in orientation statistics, J. Roy. Statist. Soc. Ser. B, 39, 95 Lehmann, 1986 Luke, 1969, Vol. 1 MacKenzie, 1957, The estimation of an orientation relationship, Acta Crystallogr., 10, 61, 10.1107/S0365110X57000146 Muirhead, 1978, Latent roots and matrix variates: A review of some asymptotic results, Ann. Statist., 6, 5, 10.1214/aos/1176344063 Muirhead, 1982 Prentice, 1986, Orientation statistics without parametric assumptions, J. Roy. Statist. Soc. Ser. B, 48, 214 Rivest, 1989, Spherical regression for concentrated Fisher-von Mises distributions, Ann. Statist., 17, 307, 10.1214/aos/1176347018 Stephens, 1979, Vector correlation, Biometrika, 66, 41, 10.1093/biomet/66.1.41 Sukhatme, 1970 Wahba, 1966, Section on problems and solutions: A least squares estimate of satellite attitude, SIAM Rev., 8, 384, 10.1137/1008080 Watson, 1983