7,662 research outputs found
Shape Theory via QR decomposition
This work sets the non isotropic noncentral elliptical shape distributions
via QR decomposition in the context of zonal polynomials, avoiding the
invariant polynomials and the open problems for their computation. The new
shape distributions are easily computable and then the inference procedure can
be studied under exact densities instead under the published approximations and
asymptotic densities under isotropic models. An application in Biology is
studied under the classical gaussian approach and a two non gaussian models.Comment: 13 page
Shape Theory Via SV Decomposition II
The non isotropic and non central elliptical shape distributions via the Le
and Kendall SVD decomposition approach are derived in this paper in the context
of invariant polynomials and zonal polynomials. The so termed cone and disk
densities here obtained generalise some results of the literature. Finally,
some particular densities are applied in a classical data of Biology, and the
inference is performed after choosing the best model by using a modified BIC
criterion.Comment: 16 page
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