The complex Bingham quartic distribution and shape analysis
成果类型：
Article
署名作者：
Kent, J. T.; Mardia, K. V.; McDonnell, P.
署名单位：
University of Leeds
刊物名称：
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
ISSN/ISSBN：
1369-7412
DOI：
10.1111/j.1467-9868.2006.00565.x
发表日期：
2006
页码：
747-765
关键词：
摘要：
The complex Bingham distribution was introduced by Kent as a tractable model for landmark-based shape analysis. It forms an exponential family with a sufficient statistic which is quadratic in the data. However, the distribution has too much symmetry to be widely useful. In particular, under high concentration it behaves asymptotically as a normal distribution, but where the covariance matrix is constrained to have complex symmetry. To overcome this limitation and to provide a full range of asymptotic normal behaviour, we introduce a new 'complex Bingham quartic distribution' by adding a selection of quartic terms to the log-density. In the simplest case this new distribution corresponds to Kent's FB5-distribution. Asymptotic and saddlepoint methods are developed for the normalizing constant to facilitate maximum likelihood estimation. Examples are given to show the usefulness of this new distribution.