Abstract
The statistical shape theory via QR decomposition and based on Gaussian and isotropic models is extended in this paper to the families of non-isotropic elliptical distributions. The new shape distributions are easily computable and then the inference procedure can be studied with the resulting exact densities. An application in Biology is studied under two Kotz models, the best distribution (non-Gaussian) is selected by using a modified Bayesian information criterion (BIC)*.
Acknowledgements
The authors thank the editor and the anonymous reviewers for their constructive comments and suggestions on an earlier version of this manuscript which led to this much improved version. This research work was supported by University of Medellin (Medellin, Colombia) and Universidad Autónoma Agraria Antonio Narro (México), joint Grant No. 469. Also, the first author was partially supported IDI-Spain, Grants No. FQM2006-2271 and MTM2008-05785 and the paper was written during J. A. Díaz-xGarcía's stay as a visiting professor at the Department of Statistics and O. R. of the University of Granada, Spain. F. Caro thanks the project No. 105657 of CONACYT, México.