ESTIMATION OF THE CONCENTRATION PARAMETERS OF THE FISHER MATRIX DISTRIBUTION ON 50(3) AND THE BINGHAM DISTRIBUTION ONSq,q≥ 2
作者:
Andrew T.A. Wood,
期刊:
Australian Journal of Statistics
(WILEY Available online 1993)
卷期:
Volume 35,
issue 1
页码: 69-79
ISSN:0004-9581
年代: 1993
DOI:10.1111/j.1467-842X.1993.tb01313.x
出版商: Blackwell Publishing Ltd
关键词: Bingham distribution;Fisher matrix distribution;maximum likelihood;orientation;pseudo likelihood;rotation
数据来源: WILEY
摘要:
SummaryTwo procedures are considered for estimating the concentration parameters of the Fisher matrix distribution for rotations or orientations in three dimensions. The first is maximum likelihood. The use of a convenient 1‐dimensional integral representation of the normalising constant, which greatly simplifies the computation, is suggested. The second approach exploits the equivalence of the Fisher distribution for rotations in three dimensions, and the Bingham distribution for axes in four dimensions. We describe a pseudo likelihood procedure which works for the Bingham distribution in any dimension. This alternative approach does not require numerical integration. Results on the asymptotic efficiency of the pseudo likelihood estimator relative to the maximum likelihood estimator are given, and the two estimators are compared in the analysis of a well‐known vectorcardiography data
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