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 distribution...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2013
- Institución:
- Universidad de Medellín
- Repositorio:
- Repositorio UDEM
- Idioma:
- eng
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- oai:repository.udem.edu.co:11407/3449
- Acceso en línea:
- http://hdl.handle.net/11407/3449
- Palabra clave:
- Shape theory
Maximum likelihood estimators
Zonal polynomials
Pseudo-Wishart distribution
Singular matrix multivariate distribution
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- http://purl.org/coar/access_right/c_16ec
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Generalised Shape Theory Via Pseudo-Wishart Distribution |
| dc.subject.spa.fl_str_mv |
Shape theory Maximum likelihood estimators Zonal polynomials Pseudo-Wishart distribution Singular matrix multivariate distribution |
| topic |
Shape theory Maximum likelihood estimators Zonal polynomials Pseudo-Wishart distribution Singular matrix multivariate distribution |
| spellingShingle |
Shape theory Maximum likelihood estimators Zonal polynomials Pseudo-Wishart distribution Singular matrix multivariate distribution |
| description |
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. |
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2013 |
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2013 |
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2017-06-15T22:05:22Z |
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2017-06-15T22:05:22Z |
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Article |
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http://purl.org/coar/resource_type/c_6501 http://purl.org/coar/resource_type/c_2df8fbb1 |
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info:eu-repo/semantics/article |
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Díaz-García, J. A. & Caro-Lopera, F. J. (2008) Sankhyā: The Indian Journal of Statistics, Series A Vol. 75, No. 2 (August 2013), pp. 253-276 |
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0976836X |
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http://hdl.handle.net/11407/3449 |
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DOI: 10.1007/s13171-013-0024-1 |
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09768378 |
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Díaz-García, J. A. & Caro-Lopera, F. J. (2008) Sankhyā: The Indian Journal of Statistics, Series A Vol. 75, No. 2 (August 2013), pp. 253-276 0976836X DOI: 10.1007/s13171-013-0024-1 09768378 |
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http://hdl.handle.net/11407/3449 |
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eng |
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eng |
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https://link.springer.com/article/10.1007/s13171-013-0024-1 |
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Sankhyā: The Indian Journal of Statistics. 2013, Volume 75-A, Part 2, pp. 253-276 |
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bhattacharya, a. (2008). Statistical analysis on manifolds: A non-parametric approach for inference on shape spaces. Sankhya, Ser. A, Part 2, 70, 223–266. billingsley, p. (1986). Probability and Measure. John Wiley & Sons, New York. caro-lopera, f.j., d´ıaz-garc´ıa, j.a. and gonza´lez-far´ıas, g. (2009). Noncentral elliptical configuration density. J. Multivariate Anal., 101, 32–43. davis, a.w. (1980). Invariant polynomials with two matrix arguments, extending the zonal polynomials. In Multivariate Analysis V, (P. R. Krishnaiah, ed.). North- Holland. d´ıaz-garc´ıa, j.a. and gonza´lez-far´ıas, g. (2005). Singular random matrix decompo- sitions: Distributions. J. Multivariate Anal., 194, 109–122. d´ıaz-garc´ıa, j.a. and gutie´rrez-ja´imez, r. (1997). Proof of the conjectures of H. Uhlig on the singular multivariate beta and the jacobian of a certain matrix trans- formation. Ann. Statist., 25, 2018–2023. d´ıaz-garc´ıa, j.a. and gutie´rrez-ja´imez, 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. d´ıaz-garc´ıa, j.a., gutie´rrez-ja´imez, r. and mardia, k.v. (1997). Wishart and Pseudo-Wishart distributions and some applications to shape theory. J. Multivari- ate Anal., 63, 73–87. dryden, i.l. and mardia, k.v. (1989.) Statistical shape analysis. John Wiley and Sons, Chichester. fang, k.t. and zhang, y.t. (1990). Generalized Multivariate Analysis. Science Press, Springer-Verlag, Beijing. goodall, c.g. (1991). Procustes methods in the statistical analysis of shape (with discussion). J. Roy. Statist. Soc. Ser. B, 53, 285–339. goodall, c.g. and mardia, k.v. (1993). Multivariate Aspects of Shape Theory. Ann.Statist., 21, 848–866. gupta, a.k. and varga, t. (1993). Elliptically Contoured Models in Statistics. Kluwer Academic Publishers, Dordrecht. james, a.t. (1964). Distributions of matrix variate and latent roots derived from normal samples. Ann. Math. Statist., 35, 475–501. kass, r.e. and raftery, a.e. (1995). Bayes factor. J. Amer. Statist. Soc., 90, 773–795. khatri, c.g. (1968). Some results for the singular normal multivariate regression models. Sankhy¯a A, 30, 267–280. koev, p. and edelman, a. (2006). The efficient evaluation of the hypergeometric function of a matrix argument. Math. Comp., 75, 833–846. le, h.l. and kendall, d.g. (1993). The Riemannian structure of Euclidean spaces: a novel environment for statistics. Ann. Statist., 21, 1225–1271. mardia, k.v. and dryden, i.l. (1989). The Statistical Analysis of Shape Data. Biometrika, 76, 271–281 muirhead, r.j. (1982). Aspects of multivariate statistical theory. Wiley Series in Prob- ability and Mathematical Statistics. John Wiley & Sons, Inc. raftery, a.e. (1995). Bayesian model selection in social research. Sociological Method- ology, 25, 111–163. rao, c.r. (1973). Linear statistical inference and its applications (2nd ed.). John Wiley & Sons, New York. rissanen, j. (1978). Modelling by shortest data description. Automatica, 14, 465–471. uhlig, h. (1994). On singular Wishart and singular multivariate Beta distributions. Ann. Statist., 22, 395–405. yang, ch.ch. and yang, ch.ch. (2007). Separating latent classes by information criteria. J. Classification, 24, 183–203. |
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Springer on behalf of the Indian Statistical Institute |
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Tronco común Ingenierías |
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2017-06-15T22:05:22Z2017-06-15T22:05:22Z2013Díaz-García, J. A. & Caro-Lopera, F. J. (2008) Sankhyā: The Indian Journal of Statistics, Series A Vol. 75, No. 2 (August 2013), pp. 253-2760976836Xhttp://hdl.handle.net/11407/3449DOI: 10.1007/s13171-013-0024-109768378The 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.eng Springer on behalf of the Indian Statistical InstituteTronco común IngenieríasFacultad de Ciencias Básicashttps://link.springer.com/article/10.1007/s13171-013-0024-1Sankhyā: The Indian Journal of Statistics. 2013, Volume 75-A, Part 2, pp. 253-276bhattacharya, a. (2008). Statistical analysis on manifolds: A non-parametric approach for inference on shape spaces. Sankhya, Ser. A, Part 2, 70, 223–266.billingsley, p. (1986). Probability and Measure. John Wiley & Sons, New York.caro-lopera, f.j., d´ıaz-garc´ıa, j.a. and gonza´lez-far´ıas, g. (2009). Noncentral elliptical configuration density. J. Multivariate Anal., 101, 32–43.davis, a.w. (1980). Invariant polynomials with two matrix arguments, extending the zonal polynomials. In Multivariate Analysis V, (P. R. Krishnaiah, ed.). North- Holland.d´ıaz-garc´ıa, j.a. and gonza´lez-far´ıas, g. (2005). Singular random matrix decompo- sitions: Distributions. J. Multivariate Anal., 194, 109–122.d´ıaz-garc´ıa, j.a. and gutie´rrez-ja´imez, r. (1997). Proof of the conjectures of H. Uhlig on the singular multivariate beta and the jacobian of a certain matrix trans- formation. Ann. Statist., 25, 2018–2023.d´ıaz-garc´ıa, j.a. and gutie´rrez-ja´imez, 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.d´ıaz-garc´ıa, j.a., gutie´rrez-ja´imez, r. and mardia, k.v. (1997). Wishart and Pseudo-Wishart distributions and some applications to shape theory. J. Multivari- ate Anal., 63, 73–87.dryden, i.l. and mardia, k.v. (1989.) Statistical shape analysis. John Wiley and Sons, Chichester.fang, k.t. and zhang, y.t. (1990). Generalized Multivariate Analysis. Science Press, Springer-Verlag, Beijing.goodall, c.g. (1991). Procustes methods in the statistical analysis of shape (with discussion). J. Roy. Statist. Soc. Ser. B, 53, 285–339.goodall, c.g. and mardia, k.v. (1993). Multivariate Aspects of Shape Theory. Ann.Statist., 21, 848–866.gupta, a.k. and varga, t. (1993). Elliptically Contoured Models in Statistics. Kluwer Academic Publishers, Dordrecht.james, a.t. (1964). Distributions of matrix variate and latent roots derived from normal samples. Ann. Math. Statist., 35, 475–501.kass, r.e. and raftery, a.e. (1995). Bayes factor. J. Amer. Statist. Soc., 90, 773–795.khatri, c.g. (1968). Some results for the singular normal multivariate regression models.Sankhy¯a A, 30, 267–280.koev, p. and edelman, a. (2006). The efficient evaluation of the hypergeometric function of a matrix argument. Math. Comp., 75, 833–846.le, h.l. and kendall, d.g. (1993). The Riemannian structure of Euclidean spaces: a novel environment for statistics. Ann. Statist., 21, 1225–1271.mardia, k.v. and dryden, i.l. (1989). The Statistical Analysis of Shape Data.Biometrika, 76, 271–281muirhead, r.j. (1982). Aspects of multivariate statistical theory. Wiley Series in Prob- ability and Mathematical Statistics. John Wiley & Sons, Inc.raftery, a.e. (1995). Bayesian model selection in social research. Sociological Method- ology, 25, 111–163.rao, c.r. (1973). Linear statistical inference and its applications (2nd ed.). John Wiley & Sons, New York.rissanen, j. (1978). Modelling by shortest data description. Automatica, 14, 465–471.uhlig, h. (1994). On singular Wishart and singular multivariate Beta distributions.Ann. Statist., 22, 395–405.yang, ch.ch. and yang, ch.ch. (2007). Separating latent classes by information criteria. J. Classification, 24, 183–203.Sankhyā: The Indian Journal of StatisticsShape theoryMaximum likelihood estimatorsZonal polynomialsPseudo-Wishart distributionSingular matrix multivariate distributionArticleinfo:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1info:eu-repo/semantics/restrictedAccesshttp://purl.org/coar/access_right/c_16ecGeneralised Shape Theory Via Pseudo-Wishart DistributionDíaz-García, José A.Caro-Lopera, Francisco J.Díaz-García, José A.; Universidad Autónoma AgrariaCaro-Lopera, Francisco J.; Universidad de MedellínTHUMBNAILportada.pngportada.pngimage/png17634http://repository.udem.edu.co/bitstream/11407/3449/2/portada.pngcd9e3e58a49b27c70363a569473c89e2MD52ORIGINALArticulo.htmlVer PDF en página del publicadortext/html481http://repository.udem.edu.co/bitstream/11407/3449/1/Articulo.htmldc058b2f667f3d8d988434b10fafb486MD5111407/3449oai:repository.udem.edu.co:11407/34492020-05-27 16:38:04.577Repositorio Institucional Universidad de Medellinrepositorio@udem.edu.co |