Artículo
Boente, G.; Pires, A.M.; Rodrigues, I.M. "General projection-pursuit estimators for the common principal components model: Influence functions and Monte Carlo study" (2006) Journal of Multivariate Analysis. 97(1):124-147
Este artículo es de Acceso Abierto y puede ser descargado en su versión final desde nuestro repositorio
Consulte la política de Acceso Abierto del editor
Abstract:
The common principal components (CPC) model for several groups of multivariate observations assumes equal principal axes but possibly different variances along these axes among the groups. Under a CPCs model, generalized projection-pursuit estimators are defined by using score functions on the dispersion measure considered. Their partial influence functions are obtained and asymptotic variances are derived from them. When the score function is taken equal to the logarithm, it is shown that, under a proportionality model, the eigenvector estimators are optimal in the sense of minimizing the asymptotic variance of the eigenvectors, for a given scale measure. © 2004 Elsevier Inc. All rights reserved.
Registro:
| Documento: | Artículo |
| Título: | General projection-pursuit estimators for the common principal components model: Influence functions and Monte Carlo study |
| Autor: | Boente, G.; Pires, A.M.; Rodrigues, I.M. |
| Filiación: | Facultad de Ciencias Exactas y Naturales, Departamento de Matemática, Universidad de Buenos Aires, Pabellón 1, Buenos Aires C142 8EHA, Argentina Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal |
| Palabras clave: | Asymptotic variances; Common principal components; Partial influence function; Projection-pursuit; Robust estimation |
| Año: | 2006 |
| Volumen: | 97 |
| Número: | 1 |
| Página de inicio: | 124 |
| Página de fin: | 147 |
| DOI: | http://dx.doi.org/10.1016/j.jmva.2004.11.007 |
| Título revista: | Journal of Multivariate Analysis |
| Título revista abreviado: | J. Multivariate Anal. |
| ISSN: | 0047259X |
| CODEN: | JMVAA |
| PDF: | https://bibliotecadigital.exactas.uba.ar/download/paper/paper_0047259X_v97_n1_p124_Boente.pdf |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0047259X_v97_n1_p124_Boente |
Referencias:
- Berrendero, J.R., Contribuciones a la teoría de la robustez respecto al sesgo (1996), Unpublished Ph.D. Thesis, Universidad Carlos III de Madrid (in Spanish); Boente, G., Critchley, F., Orellana, L., Influence functions for robust estimators under proportional scatter matrices Working paper, Universidad de Buenos Aires; Boente, G., Orellana, L., A robust approach to common principal components (2001) Statistics in Genetics and in the Environmental Sciences, pp. 117-147. , L.T. Fernholz S. Morgenthaler W. Stahel (Eds.) Basel Birkhauser
- Boente, G., Pires, A.M., Rodrigues, I.M., Influence functions and outlier detection under the common principal components model: A robust approach (2002) Biometrika, 89, pp. 861-875
- Croux, C., Efficient high-breakdown M-estimators of scale (1994) Statist. Probab. Lett., 19, pp. 371-379
- Croux, C., Ruiz-Gazen, A., A fast algorithm for robust principal components based on projection pursuit (1996) Compstat: Proceedings in Computational Statistics, pp. 211-217. , A. Prat (Ed.) Physica-Verlag Heidelberg
- Croux, C., Ruiz-Gazen, A., High breakdown estimators for principal components: The projection-pursuit approach revisited (2000), Working paper, Université Libre de Bruxelles; Cui, H., He, X., Ng, K.W., Asymptotic distribution of principal components based on robust dispersions (2003) Biometrika, 90, pp. 953-966
- Flury, B.K., Common principal components in k groups (1984) J. Amer. Statist. Assoc., 79, pp. 892-898
- Flury, B.K., (1988) Common Principal Components and Related Multivariate Models, , New York: Wiley
- Huber, P., (1981) Robust Statistics, , New York: Wiley
- Li, G., Chen, Z., Projection-pursuit approach to robust dispersion matrices and principal components: Primary theory and Monte Carlo (1985) J. Amer. Statist. Assoc., 80, pp. 759-766
- Patak, Z., Robust principal components (1991), Master Thesis of the Department of Statistics, University of British Columbia, Vancouver; Pires, A.M., Branco, J., Partial influence functions (2002) J. Multivariate Anal., 83, pp. 458-468
- Rodrigues, I.M., Métodos robustos em análise de componentes principais comuns (2003), http://www.math.ist.utl.pt/apires/phd.html, Unpublished Ph.D. Thesis,Universidade Técnica de Lisboa (in Portuguese). Available on
Citas:
---------- APA ----------
Boente, G., Pires, A.M. & Rodrigues, I.M. (2006) . General projection-pursuit estimators for the common principal components model: Influence functions and Monte Carlo study. Journal of Multivariate Analysis, 97(1), 124-147.http://dx.doi.org/10.1016/j.jmva.2004.11.007
---------- CHICAGO ----------
Boente, G., Pires, A.M., Rodrigues, I.M. "General projection-pursuit estimators for the common principal components model: Influence functions and Monte Carlo study" . Journal of Multivariate Analysis 97, no. 1 (2006) : 124-147.http://dx.doi.org/10.1016/j.jmva.2004.11.007
---------- MLA ----------
Boente, G., Pires, A.M., Rodrigues, I.M. "General projection-pursuit estimators for the common principal components model: Influence functions and Monte Carlo study" . Journal of Multivariate Analysis, vol. 97, no. 1, 2006, pp. 124-147.http://dx.doi.org/10.1016/j.jmva.2004.11.007
---------- VANCOUVER ----------
Boente, G., Pires, A.M., Rodrigues, I.M. General projection-pursuit estimators for the common principal components model: Influence functions and Monte Carlo study. J. Multivariate Anal. 2006;97(1):124-147.http://dx.doi.org/10.1016/j.jmva.2004.11.007
