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

RACSAM (2003)

- Volume: 97, Issue: 1, page 41-51
- ISSN: 1578-7303

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topChakak, 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 -

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