A statistical model for random rotations |
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Authors: | Carlos A León |
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Institution: | Département de Mathématiques et de Statistique, Université Laval, Qué., Canada G1K 7P4 |
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Abstract: | This paper studies the properties of the Cayley distributions, a new family of models for random p×p rotations. This class of distributions is related to the Cayley transform that maps a p(p-1)/2×1 vector s into SO(p), the space of p×p rotation matrices. First an expression for the uniform measure on SO(p) is derived using the Cayley transform, then the Cayley density for random rotations is investigated. A closed-form expression is derived for its normalizing constant, a simple simulation algorithm is proposed, and moments are derived. The efficiencies of moment estimators of the parameters of the new model are also calculated. A Monte Carlo investigation of tests and of confidence regions for the parameters of the new density is briefly summarized. A numerical example is presented. |
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Keywords: | 62H11 62H05 |
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