Navegar

Colección

Datos Estadísticas

Artículo

Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

The asymptotic distribution of the eigenvalues and eigenvectors of the robust scatter matrix proposed by R. Maronna in 1976 is given when the observations are from an ellipsoidal distribution. The elements of each characteristic vector are the coefficients of a robustified version of principal components. We give a definition for the asymptotic efficiency of these estimators and we evaluate their influence curve. The problem of maximizing the efficiency under a bound on the influence curve is solved. Numerically, we calibrate the optimal estimators under the multivariate normal distribution and we evaluate their sensitivity. © 1987.

Registro:

Documento: Artículo
Título:Asymptotic theory for robust principal components
Autor:Boente, G.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Buenos Aires, Argentina
CONICET, Argentina
Palabras clave:principal components; robust estimation; robust scatter matrix
Año:1987
Volumen:21
Número:1
Página de inicio:67
Página de fin:78
DOI: http://dx.doi.org/10.1016/0047-259X(87)90099-6
Título revista:Journal of Multivariate Analysis
Título revista abreviado:J. Multivariate Anal.
ISSN:0047259X
CODEN:JMVAA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0047259X_v21_n1_p67_Boente

Referencias:

  • Anderson, (1958) An Introduction to Multivariate Statistical Analysis, , 2nd ed., Wiley, New York
  • Anderson, Asymptotic theory for principal component analysis (1963) The Annals of Mathematical Statistics, 34, pp. 122-148
  • Boente, Yohai, (1981) An optimal property of principal components without using moments, , Unpublished manuscript
  • Devlin, Gnanadesikan, Kettenring, Robust estimation of dispersion matrices and principal components (1981) Journal of the American Statistical Association, 76, pp. 354-362
  • Fang, Krishnaiah, Asymptotic distributions functions of the eigenvalues of some random matrices for non-normal populations (1982) J. Multivariate Anal., 12, pp. 39-63
  • Hampel, Contribution to the Theory of Robust Estimation (1968) Ph. D. Thesis, , 2nd ed., University of California, Berkeley
  • Hampel, The influence curve and its role in robust estimation (1974) Journal of the American Statistical Association, 69, pp. 383-393
  • Krasker, (1978) Estimation in linear regression models with disparate data points, , Unpublished paper
  • Maronna, Robust M-estimators of location and scatter (1976) The Annals of Statistics, 4, pp. 51-67
  • Tyler, The asymptotic distribution of principal components roots under local alternative to multiple roots (1983) Ann. Statist., 11, pp. 1232-1242

Citas:

---------- APA ----------
(1987) . Asymptotic theory for robust principal components. Journal of Multivariate Analysis, 21(1), 67-78.
http://dx.doi.org/10.1016/0047-259X(87)90099-6
---------- CHICAGO ----------
Boente, G. "Asymptotic theory for robust principal components" . Journal of Multivariate Analysis 21, no. 1 (1987) : 67-78.
http://dx.doi.org/10.1016/0047-259X(87)90099-6
---------- MLA ----------
Boente, G. "Asymptotic theory for robust principal components" . Journal of Multivariate Analysis, vol. 21, no. 1, 1987, pp. 67-78.
http://dx.doi.org/10.1016/0047-259X(87)90099-6
---------- VANCOUVER ----------
Boente, G. Asymptotic theory for robust principal components. J. Multivariate Anal. 1987;21(1):67-78.
http://dx.doi.org/10.1016/0047-259X(87)90099-6