Generalised shape theory via SV decomposition I
This work finds in terms of zonal polynomials, the non isotropic noncentral elliptical shape distributions via singular value decomposition; it avoids the invariant polynomials and the open problems for their computation. The new shape distributions are easily computable and then the inference proce...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2012
- Institución:
- Universidad de Medellín
- Repositorio:
- Repositorio UDEM
- Idioma:
- eng
- OAI Identifier:
- oai:repository.udem.edu.co:11407/3405
- Acceso en línea:
- http://hdl.handle.net/11407/3405
- Palabra clave:
- Shape theory
Non-central and non-isotropic shape densities
Zonal polynomials
- Rights
- restrictedAccess
- License
- http://purl.org/coar/access_right/c_16ec
| id |
REPOUDEM2_f3d6f92f5ce453d031e4ab59fe93c9fd |
|---|---|
| oai_identifier_str |
oai:repository.udem.edu.co:11407/3405 |
| network_acronym_str |
REPOUDEM2 |
| network_name_str |
Repositorio UDEM |
| repository_id_str |
|
| spelling |
2017-06-15T22:05:18Z2017-06-15T22:05:18Z2012Díaz-García, J. A., & Caro-Lopera, F. J. (2012). Generalised shape theory via SV decomposition I. Metrika, 75(4), 541-565.00261335http://hdl.handle.net/11407/3405DOI: 10.1007/s00184-010-0341-51435926XThis work finds in terms of zonal polynomials, the non isotropic noncentral elliptical shape distributions via singular value decomposition; it avoids the invariant polynomials and the open problems for their computation. The new shape distributions are easily computable and then the inference procedure is based on exact densities, instead of the published approximations and asymptotic distribution of isotropic models. An application of the technique is illustrated with a classical landmark data of Biology, for this, three Kotz type models are proposed (including Gaussian); then the best one is chosen by using a modified BIC criterion.engPhysica-Verlag Gmbh und CoSpringer Berlin HeidelbergTronco común IngenieríasFacultad de Ciencias Básicashttps://link.springer.com/article/10.1007%2Fs00184-010-0341-5?LI=trueMetrika, May 2012, Volume 75, Issue 4, pp 541–565Caro-Lopera FJ, Díaz-García JA, González-Farías G (2009) Noncentral elliptical configuration density. J Multivar Anal 101(1): 32–43Davis AW (1980) Invariant polynomials with two matrix arguments, extending the zonal polynomials. In: Krishnaiah PR (ed.) Multivariate analysis V. North-Holland Publishing Company, Amsterdam, pp 287–299Díaz-García JA, Gutiérrez- Jáimez R, Mardia KV (1997) Wishart and Pseudo-Wishart distributions and some applications to shape theory. J Multivar Anal 63: 73–87Díaz-García JA, Gutiérrez-Jáimez R, Ramos R (2003) Size-and-shape cone, shape disk and configuration densities for the elliptical models. Braz J Probab Stat 17: 135–146Dryden IL, Mardia KV (1998) Statistical shape analysis. Wiley, ChichesterFang KT, Zhang YT (1990) Generalized multivariate analysis. Science Press, Springer, BeijingGoodall CR (1991) Procustes methods in the statistical analysis of shape (with discussion). J R Stat Soc Ser B 53: 285–339Goodall CR, Mardia KV (1993) Multivariate aspects of shape theory. Ann Stat 21: 848–866Gupta AK, Varga T (1993) Elliptically contoured models in statistics. Kluwer, DordrechtJames AT (1964) Distributions of matrix variate and latent roots derived from normal samples. Ann Math Stat 35: 475–501Kass RE, Raftery AE (1995) Bayes factor. J Am Stat Soc 90: 773–795Koev P, Edelman A (2006) The efficient evaluation of the hypergeometric function of a matrix argument. Math Comput 75: 833–846Le HL, Kendall DG (1993) The Riemannian structure of Euclidean spaces: a novel environment for statistics. Ann Stat 21: 1225–1271Mardia KV, Dryden IL (1989) The statistical analysis of shape data. Biometrika 76(2): 271–281Muirhead RJ (1982) Aspects of multivariate statistical theory. Wiley series in probability and mathematical statistics. Wiley, New YorkRaftery AE (1995) Bayesian model selection in social research. Sociol Methodol 25: 111–163Rissanen J (1978) Modelling by shortest data description. Automatica 14: 465–471Yang ChCh, Yang ChCh (2007) Separating latent classes by information criteria. J Classif 24: 183–203Metrika: International Journal for Theoretical and Applied StatisticsShape theoryNon-central and non-isotropic shape densitiesZonal polynomialsGeneralised shape theory via SV decomposition IArticleinfo: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_16ecDíaz-García, José A.Caro-Lopera, Francisco J.Díaz-García, José A.; Universidad Autónoma Agraria Antonio NarroCaro-Lopera, Francisco J.; Universidad de MedellínORIGINALArticulo.htmltext/html501http://repository.udem.edu.co/bitstream/11407/3405/1/Articulo.html4ea1cbe0827e7beb03631908d62a1690MD5111407/3405oai:repository.udem.edu.co:11407/34052020-05-27 19:17:34.871Repositorio Institucional Universidad de Medellinrepositorio@udem.edu.co |
| dc.title.spa.fl_str_mv |
Generalised shape theory via SV decomposition I |
| title |
Generalised shape theory via SV decomposition I |
| spellingShingle |
Generalised shape theory via SV decomposition I Shape theory Non-central and non-isotropic shape densities Zonal polynomials |
| title_short |
Generalised shape theory via SV decomposition I |
| title_full |
Generalised shape theory via SV decomposition I |
| title_fullStr |
Generalised shape theory via SV decomposition I |
| title_full_unstemmed |
Generalised shape theory via SV decomposition I |
| title_sort |
Generalised shape theory via SV decomposition I |
| dc.subject.spa.fl_str_mv |
Shape theory Non-central and non-isotropic shape densities Zonal polynomials |
| topic |
Shape theory Non-central and non-isotropic shape densities Zonal polynomials |
| description |
This work finds in terms of zonal polynomials, the non isotropic noncentral elliptical shape distributions via singular value decomposition; it avoids the invariant polynomials and the open problems for their computation. The new shape distributions are easily computable and then the inference procedure is based on exact densities, instead of the published approximations and asymptotic distribution of isotropic models. An application of the technique is illustrated with a classical landmark data of Biology, for this, three Kotz type models are proposed (including Gaussian); then the best one is chosen by using a modified BIC criterion. |
| publishDate |
2012 |
| dc.date.created.none.fl_str_mv |
2012 |
| dc.date.accessioned.none.fl_str_mv |
2017-06-15T22:05:18Z |
| dc.date.available.none.fl_str_mv |
2017-06-15T22:05:18Z |
| dc.type.eng.fl_str_mv |
Article |
| dc.type.coar.fl_str_mv |
http://purl.org/coar/resource_type/c_6501 http://purl.org/coar/resource_type/c_2df8fbb1 |
| dc.type.driver.none.fl_str_mv |
info:eu-repo/semantics/article |
| dc.identifier.citation.spa.fl_str_mv |
Díaz-García, J. A., & Caro-Lopera, F. J. (2012). Generalised shape theory via SV decomposition I. Metrika, 75(4), 541-565. |
| dc.identifier.issn.none.fl_str_mv |
00261335 |
| dc.identifier.uri.none.fl_str_mv |
http://hdl.handle.net/11407/3405 |
| dc.identifier.doi.none.fl_str_mv |
DOI: 10.1007/s00184-010-0341-5 |
| dc.identifier.eissn.none.fl_str_mv |
1435926X |
| identifier_str_mv |
Díaz-García, J. A., & Caro-Lopera, F. J. (2012). Generalised shape theory via SV decomposition I. Metrika, 75(4), 541-565. 00261335 DOI: 10.1007/s00184-010-0341-5 1435926X |
| url |
http://hdl.handle.net/11407/3405 |
| dc.language.iso.none.fl_str_mv |
eng |
| language |
eng |
| dc.relation.isversionof.spa.fl_str_mv |
https://link.springer.com/article/10.1007%2Fs00184-010-0341-5?LI=true |
| dc.relation.ispartofes.spa.fl_str_mv |
Metrika, May 2012, Volume 75, Issue 4, pp 541–565 |
| dc.relation.references.spa.fl_str_mv |
Caro-Lopera FJ, Díaz-García JA, González-Farías G (2009) Noncentral elliptical configuration density. J Multivar Anal 101(1): 32–43 Davis AW (1980) Invariant polynomials with two matrix arguments, extending the zonal polynomials. In: Krishnaiah PR (ed.) Multivariate analysis V. North-Holland Publishing Company, Amsterdam, pp 287–299 Díaz-García JA, Gutiérrez- Jáimez R, Mardia KV (1997) Wishart and Pseudo-Wishart distributions and some applications to shape theory. J Multivar Anal 63: 73–87 Díaz-García JA, Gutiérrez-Jáimez R, Ramos R (2003) Size-and-shape cone, shape disk and configuration densities for the elliptical models. Braz J Probab Stat 17: 135–146 Dryden IL, Mardia KV (1998) Statistical shape analysis. Wiley, Chichester Fang KT, Zhang YT (1990) Generalized multivariate analysis. Science Press, Springer, Beijing Goodall CR (1991) Procustes methods in the statistical analysis of shape (with discussion). J R Stat Soc Ser B 53: 285–339 Goodall CR, Mardia KV (1993) Multivariate aspects of shape theory. Ann Stat 21: 848–866 Gupta AK, Varga T (1993) Elliptically contoured models in statistics. Kluwer, Dordrecht James AT (1964) Distributions of matrix variate and latent roots derived from normal samples. Ann Math Stat 35: 475–501 Kass RE, Raftery AE (1995) Bayes factor. J Am Stat Soc 90: 773–795 Koev P, Edelman A (2006) The efficient evaluation of the hypergeometric function of a matrix argument. Math Comput 75: 833–846 Le HL, Kendall DG (1993) The Riemannian structure of Euclidean spaces: a novel environment for statistics. Ann Stat 21: 1225–1271 Mardia KV, Dryden IL (1989) The statistical analysis of shape data. Biometrika 76(2): 271–281 Muirhead RJ (1982) Aspects of multivariate statistical theory. Wiley series in probability and mathematical statistics. Wiley, New York Raftery AE (1995) Bayesian model selection in social research. Sociol Methodol 25: 111–163 Rissanen J (1978) Modelling by shortest data description. Automatica 14: 465–471 Yang ChCh, Yang ChCh (2007) Separating latent classes by information criteria. J Classif 24: 183–203 |
| dc.rights.coar.fl_str_mv |
http://purl.org/coar/access_right/c_16ec |
| dc.rights.accessrights.none.fl_str_mv |
info:eu-repo/semantics/restrictedAccess |
| eu_rights_str_mv |
restrictedAccess |
| rights_invalid_str_mv |
http://purl.org/coar/access_right/c_16ec |
| dc.publisher.spa.fl_str_mv |
Physica-Verlag Gmbh und Co Springer Berlin Heidelberg |
| dc.publisher.program.spa.fl_str_mv |
Tronco común Ingenierías |
| dc.publisher.faculty.spa.fl_str_mv |
Facultad de Ciencias Básicas |
| dc.source.spa.fl_str_mv |
Metrika: International Journal for Theoretical and Applied Statistics |
| institution |
Universidad de Medellín |
| bitstream.url.fl_str_mv |
http://repository.udem.edu.co/bitstream/11407/3405/1/Articulo.html |
| bitstream.checksum.fl_str_mv |
4ea1cbe0827e7beb03631908d62a1690 |
| bitstream.checksumAlgorithm.fl_str_mv |
MD5 |
| repository.name.fl_str_mv |
Repositorio Institucional Universidad de Medellin |
| repository.mail.fl_str_mv |
repositorio@udem.edu.co |
| _version_ |
1814159270034276352 |