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Statistical theory of shape under elliptical models via QR decomposition |
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| Authors: | José A Díaz-García Francisco J Caro-Lopera |
| Institution: | 1. Department of Statistics and Computation, Universidad Autónoma, Agraria Antonio Narro, 25350 Buenavista, Saltillo, Coahuila, México;2. jadiaz@uaaan.mx;4. Department of Basic Sciences, Universidad de Medellín, Carrera 87, No.30-65, of. 5-103, Medellín, Colombia |
| 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)*. |
| Keywords: | shape theory maximum likelihood estimators non-central and non-isotropic shape density QR decomposition zonal polynomials |