A mathematical correction problem
Jerzy Zabczyk (1972)
Kybernetika
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Jerzy Zabczyk (1972)
Kybernetika
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Anton Bovier, Irina Kurkova (2004)
Annales de l'I.H.P. Probabilités et statistiques
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M. Fisz (1958)
Studia Mathematica
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Petr Mandl, Ma.Rosario Romera Ayllón (1987)
Kybernetika
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A. Chakak, L. Imhali (2003)
RACSAM
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For a random rotation X = M e where M 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)) (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...