A study of the tangent space model of the von Mises-Fisher distrubution.

Chakak, A., and Imhali, L.. "A study of the tangent space model of the von Mises-Fisher distrubution.." RACSAM 97.1 (2003): 41-51. <http://eudml.org/doc/40950>.

@article{Chakak2003,
abstract = {For a random rotation X = M0 eφ(ε) where M0 is a 3 x 3 rotation, ε is a trivariate random vector, and φ(ε) is a skew symmetric matrix, the least squares criterion consists of seeking a rotation M called the mean rotation minimizing tr[(M - E(X))t (M - E(X))]. Some conditions on the distribution of ε are set so that the least squares estimator is unbiased. Of interest is when ε is normally distributed N(0;Σ). Unbiasedness of the least squares estimator is dealt with according to eigenvalues of Σ.},
author = {Chakak, A., Imhali, L.},
journal = {RACSAM},
keywords = {Teoría de la distribución; Distribución de Von Mises; Rotación; Estimación insesgada; Mínimos cuadrados; matrix von Mises-Fiser distribution; rotation; unbiased least squares estimation; tangent approximation model},
language = {eng},
number = {1},
pages = {41-51},
title = {A study of the tangent space model of the von Mises-Fisher distrubution.},
url = {http://eudml.org/doc/40950},
volume = {97},
year = {2003},
}

TY - JOUR
AU - Chakak, A.
AU - Imhali, L.
TI - A study of the tangent space model of the von Mises-Fisher distrubution.
JO - RACSAM
PY - 2003
VL - 97
IS - 1
SP - 41
EP - 51
AB - For a random rotation X = M0 eφ(ε) where M0 is a 3 x 3 rotation, ε is a trivariate random vector, and φ(ε) is a skew symmetric matrix, the least squares criterion consists of seeking a rotation M called the mean rotation minimizing tr[(M - E(X))t (M - E(X))]. Some conditions on the distribution of ε are set so that the least squares estimator is unbiased. Of interest is when ε is normally distributed N(0;Σ). Unbiasedness of the least squares estimator is dealt with according to eigenvalues of Σ.
LA - eng
KW - Teoría de la distribución; Distribución de Von Mises; Rotación; Estimación insesgada; Mínimos cuadrados; matrix von Mises-Fiser distribution; rotation; unbiased least squares estimation; tangent approximation model
UR - http://eudml.org/doc/40950
ER -