The Maximum Bias of Robust Covariances : Notas de Matemática, 46
This paper deals with the maximum asymptotic bias of tiro classes of robust estimates of the dispersion matrix V of a p-dimensional random vector z, under a contamination model of the form P = (1—ε)Po+δ(x0), where P is the distribution of z, Po is a spherical distribution, and δ(x0) is a point mass...
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| Formato: | Publicacion seriada |
| Lenguaje: | Inglés |
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1987
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| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/168837 |
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I19-R120-10915-1688372024-08-22T04:08:07Z http://sedici.unlp.edu.ar/handle/10915/168837 The Maximum Bias of Robust Covariances : Notas de Matemática, 46 Maronna, Ricardo Antonio Yohai, Víctor Jaime 1987 2024-08-21T16:48:23Z en Matemática Robust covariance maximum bias M-estimators high breakdown point estimators This paper deals with the maximum asymptotic bias of tiro classes of robust estimates of the dispersion matrix V of a p-dimensional random vector z, under a contamination model of the form P = (1—ε)Po+δ(x0), where P is the distribution of z, Po is a spherical distribution, and δ(x0) is a point mass at z0. Estimators VQ,α of the first class minimise the α quantile of x´V-1z among all symmetric positive-definite matrices V for some α ϵ (0,1). The "maximum volume ellipsoid" estimator proposed by Rouseauw belongs to this class with α = 0.5. These estimators have breakdown point min(α, 1 - α) for all p. The second class of estimators constat of the M-estimaton, from which the seemingly most robust member was choses; namely the Tyler estimate defined as the solution VT of Ez´VT-1z/z´z = VT. This estimator has breakdown point 1/p. The numerical results show that except for ε very close to 1/p, VT has in general a smaller máximum bias than VQ,α; and that the maximum bias of the latter may be extremely large even for a much smaller than its breakdown point. Material digitalizado en SEDICI gracias a la colaboración de la Biblioteca del Departamento de Matemática de la Facultad de Ciencias Exactas (UNLP). Facultad de Ciencias Exactas Publicacion seriada Publicacion seriada http://creativecommons.org/licenses/by-nc-sa/4.0/ Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) application/pdf |
| institution |
Universidad Nacional de La Plata |
| institution_str |
I-19 |
| repository_str |
R-120 |
| collection |
SEDICI (UNLP) |
| language |
Inglés |
| topic |
Matemática Robust covariance maximum bias M-estimators high breakdown point estimators |
| spellingShingle |
Matemática Robust covariance maximum bias M-estimators high breakdown point estimators Maronna, Ricardo Antonio Yohai, Víctor Jaime The Maximum Bias of Robust Covariances : Notas de Matemática, 46 |
| topic_facet |
Matemática Robust covariance maximum bias M-estimators high breakdown point estimators |
| description |
This paper deals with the maximum asymptotic bias of tiro classes of robust estimates of the dispersion matrix V of a p-dimensional random vector z, under a contamination model of the form P = (1—ε)Po+δ(x0), where P is the distribution of z, Po is a spherical distribution, and δ(x0) is a point mass at z0. Estimators VQ,α of the first class minimise the α quantile of x´V-1z among all symmetric positive-definite matrices V for some α ϵ (0,1). The "maximum volume ellipsoid" estimator proposed by Rouseauw belongs to this class with α = 0.5. These estimators have breakdown point min(α, 1 - α) for all p. The second class of estimators constat of the M-estimaton, from which the seemingly most robust member was choses; namely the Tyler estimate defined as the solution VT of Ez´VT-1z/z´z = VT. This estimator has breakdown point 1/p. The numerical results show that except for ε very close to 1/p, VT has in general a smaller máximum bias than VQ,α; and that the maximum bias of the latter may be extremely large even for a much smaller than its breakdown point. |
| format |
Publicacion seriada Publicacion seriada |
| author |
Maronna, Ricardo Antonio Yohai, Víctor Jaime |
| author_facet |
Maronna, Ricardo Antonio Yohai, Víctor Jaime |
| author_sort |
Maronna, Ricardo Antonio |
| title |
The Maximum Bias of Robust Covariances : Notas de Matemática, 46 |
| title_short |
The Maximum Bias of Robust Covariances : Notas de Matemática, 46 |
| title_full |
The Maximum Bias of Robust Covariances : Notas de Matemática, 46 |
| title_fullStr |
The Maximum Bias of Robust Covariances : Notas de Matemática, 46 |
| title_full_unstemmed |
The Maximum Bias of Robust Covariances : Notas de Matemática, 46 |
| title_sort |
maximum bias of robust covariances : notas de matemática, 46 |
| publishDate |
1987 |
| url |
http://sedici.unlp.edu.ar/handle/10915/168837 |
| work_keys_str_mv |
AT maronnaricardoantonio themaximumbiasofrobustcovariancesnotasdematematica46 AT yohaivictorjaime themaximumbiasofrobustcovariancesnotasdematematica46 AT maronnaricardoantonio maximumbiasofrobustcovariancesnotasdematematica46 AT yohaivictorjaime maximumbiasofrobustcovariancesnotasdematematica46 |
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