Asymptotic theory for robust principal components
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 compo...
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todo:paper_0047259X_v21_n1_p67_Boente2023-10-03T14:52:23Z Asymptotic theory for robust principal components Boente, G. principal components robust estimation robust scatter matrix 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. Fil:Boente, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0047259X_v21_n1_p67_Boente |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
principal components robust estimation robust scatter matrix |
| spellingShingle |
principal components robust estimation robust scatter matrix Boente, G. Asymptotic theory for robust principal components |
| topic_facet |
principal components robust estimation robust scatter matrix |
| description |
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. |
| format |
JOUR |
| author |
Boente, G. |
| author_facet |
Boente, G. |
| author_sort |
Boente, G. |
| title |
Asymptotic theory for robust principal components |
| title_short |
Asymptotic theory for robust principal components |
| title_full |
Asymptotic theory for robust principal components |
| title_fullStr |
Asymptotic theory for robust principal components |
| title_full_unstemmed |
Asymptotic theory for robust principal components |
| title_sort |
asymptotic theory for robust principal components |
| url |
http://hdl.handle.net/20.500.12110/paper_0047259X_v21_n1_p67_Boente |
| work_keys_str_mv |
AT boenteg asymptotictheoryforrobustprincipalcomponents |
| _version_ |
1782024063025152000 |