Skip to main content
Log in

Generalised Shape Theory Via Pseudo-Wishart Distribution

  • Published:
Sankhya A Aims and scope Submit manuscript

Abstract

The non isotropic noncentral elliptical shape distributions via pseudo-Wishart distribution are founded. This way, the classical shape theory is extended to non isotropic case and the normality assumption is replaced by assuming a elliptical distribution. In several cases, the new shape distributions are easily computable and then the inference procedure can be studied under exact densities. An application in Biology is studied under the classical gaussian approach and two non gaussian models.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Bhattacharya, A. (2008). Statistical analysis on manifolds: A non-parametric approach for inference on shape spaces. Sankhya, Ser. A, Part 2, 70, 223–266.

    MATH  Google Scholar 

  • Billingsley, P. (1986). Probability and Measure. John Wiley & Sons, New York.

    MATH  Google Scholar 

  • Caro-Lopera, F.J., Díaz-García, J.A. and González-Farías, G. (2009). Noncentral elliptical configuration density. J. Multivariate Anal., 101, 32–43.

    Article  Google Scholar 

  • Davis, A.W. (1980). Invariant polynomials with two matrix arguments, extending the zonal polynomials. In Multivariate Analysis V, (P. R. Krishnaiah, ed.). North-Holland.

  • Díaz-García, J.A. and González-Farías, G. (2005). Singular random matrix decompositions: Distributions. J. Multivariate Anal., 194, 109–122.

    Article  Google Scholar 

  • Díaz-García, J.A. and Gutiérrez-Jáimez, R. (1997). Proof of the conjectures of H. Uhlig on the singular multivariate beta and the jacobian of a certain matrix transformation. Ann. Statist., 25, 2018–2023.

    Article  MathSciNet  MATH  Google Scholar 

  • Díaz-García, J.A. and Gutiérrez-Jáimez, R. (2006). Wishart and Pseudo-Wishart distributions under elliptical laws and related distributions in the shape theory context. J. Statist. Plann. Inference, 136, 4176–4193.

    Article  MathSciNet  MATH  Google Scholar 

  • Díaz-García, J.A., Gutiérrez-Jáimez, R. and Mardia, K.V. (1997). Wishart and Pseudo-Wishart distributions and some applications to shape theory. J. Multivariate Anal., 63, 73–87.

    Article  MathSciNet  MATH  Google Scholar 

  • Dryden, I.L. and Mardia, K.V. (1989). Statistical shape analysis. John Wiley and Sons, Chichester.

    Google Scholar 

  • Fang, K.T. and Zhang, Y.T. (1990). Generalized Multivariate Analysis. Science Press, Springer-Verlag, Beijing.

    MATH  Google Scholar 

  • Goodall, C.G. (1991). Procustes methods in the statistical analysis of shape (with discussion). J. Roy. Statist. Soc. Ser. B, 53, 285–339.

    MathSciNet  MATH  Google Scholar 

  • Goodall, C.G. and Mardia, K.V. (1993). Multivariate Aspects of Shape Theory. Ann. Statist., 21, 848–866.

    Article  MathSciNet  MATH  Google Scholar 

  • Gupta, A.K. and Varga, T. (1993). Elliptically Contoured Models in Statistics. Kluwer Academic Publishers, Dordrecht.

    Book  MATH  Google Scholar 

  • James, A.T. (1964). Distributions of matrix variate and latent roots derived from normal samples. Ann. Math. Statist., 35, 475–501.

    Article  MathSciNet  MATH  Google Scholar 

  • Kass, R.E. and Raftery, A.E. (1995). Bayes factor. J. Amer. Statist. Soc., 90, 773–795.

    Article  MATH  Google Scholar 

  • Khatri, C.G. (1968). Some results for the singular normal multivariate regression models. Sankhyā A, 30, 267–280.

    MATH  Google Scholar 

  • Koev, P. and Edelman, A. (2006). The efficient evaluation of the hypergeometric function of a matrix argument. Math. Comp., 75, 833–846.

    Article  MathSciNet  MATH  Google Scholar 

  • Le, H.L. and Kendall, D.G. (1993). The Riemannian structure of Euclidean spaces: a novel environment for statistics. Ann. Statist., 21, 1225–1271.

    Article  MathSciNet  MATH  Google Scholar 

  • Mardia, K.V. and Dryden, I.L. (1989). The Statistical Analysis of Shape Data. Biometrika, 76, 271–281

    Article  MathSciNet  MATH  Google Scholar 

  • Muirhead, R.J. (1982). Aspects of multivariate statistical theory. Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons, Inc.

  • Raftery, A.E. (1995). Bayesian model selection in social research. Sociological Methodology, 25, 111–163.

    Article  Google Scholar 

  • Rao, C.R. (1973). Linear statistical inference and its applications (2nd ed.). John Wiley & Sons, New York.

    Book  MATH  Google Scholar 

  • Rissanen, J. (1978). Modelling by shortest data description. Automatica, 14, 465–471.

    Article  MATH  Google Scholar 

  • Uhlig, H. (1994). On singular Wishart and singular multivariate Beta distributions. Ann. Statist., 22, 395–405.

    Article  MathSciNet  MATH  Google Scholar 

  • Yang, Ch.Ch. and Yang, Ch.Ch. (2007). Separating latent classes by information criteria. J. Classification, 24, 183–203.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to José A. Díaz-García.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Díaz-García, J.A., Caro-Lopera, F.J. Generalised Shape Theory Via Pseudo-Wishart Distribution. Sankhya A 75, 253–276 (2013). https://doi.org/10.1007/s13171-013-0024-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13171-013-0024-1

Keywords and phrases

AMS (2000) subject classification

Navigation