Projection estimates of multivariate location
In this paper we study the maximum asymptotic bias of the projection estimate for multivariate location based on univariate estimates of location and dispersion. In particular we study the projection estimate that uses the median and median absolute deviation about the median (MAD) as univariate loc...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00905364_v30_n6_p1760_Adrover |
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todo:paper_00905364_v30_n6_p1760_Adrover2023-10-03T14:54:41Z Projection estimates of multivariate location Adrover, J. Yohai, V. Maximum bias Multivariate location Projection estimates Robust estimates In this paper we study the maximum asymptotic bias of the projection estimate for multivariate location based on univariate estimates of location and dispersion. In particular we study the projection estimate that uses the median and median absolute deviation about the median (MAD) as univariate location and dispersion estimates respectively. This estimator may be considered a natural affine equivariant multivariate median. For spherical distributions the maximum bias of this estimate depends only on the marginal distributions, and not on the dimension, and is approximately twice the maximum bias of the univariate median. We also show that for multivariate normal distributions, its maximum bias compares favorably with those of the Donoho-Stahel, minimum volume ellipsoid and minimum covariance determinant estimates. In all these cases the maximum bias increases with the dimension p. Fil:Adrover, J. 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_00905364_v30_n6_p1760_Adrover |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
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R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Maximum bias Multivariate location Projection estimates Robust estimates |
| spellingShingle |
Maximum bias Multivariate location Projection estimates Robust estimates Adrover, J. Yohai, V. Projection estimates of multivariate location |
| topic_facet |
Maximum bias Multivariate location Projection estimates Robust estimates |
| description |
In this paper we study the maximum asymptotic bias of the projection estimate for multivariate location based on univariate estimates of location and dispersion. In particular we study the projection estimate that uses the median and median absolute deviation about the median (MAD) as univariate location and dispersion estimates respectively. This estimator may be considered a natural affine equivariant multivariate median. For spherical distributions the maximum bias of this estimate depends only on the marginal distributions, and not on the dimension, and is approximately twice the maximum bias of the univariate median. We also show that for multivariate normal distributions, its maximum bias compares favorably with those of the Donoho-Stahel, minimum volume ellipsoid and minimum covariance determinant estimates. In all these cases the maximum bias increases with the dimension p. |
| format |
JOUR |
| author |
Adrover, J. Yohai, V. |
| author_facet |
Adrover, J. Yohai, V. |
| author_sort |
Adrover, J. |
| title |
Projection estimates of multivariate location |
| title_short |
Projection estimates of multivariate location |
| title_full |
Projection estimates of multivariate location |
| title_fullStr |
Projection estimates of multivariate location |
| title_full_unstemmed |
Projection estimates of multivariate location |
| title_sort |
projection estimates of multivariate location |
| url |
http://hdl.handle.net/20.500.12110/paper_00905364_v30_n6_p1760_Adrover |
| work_keys_str_mv |
AT adroverj projectionestimatesofmultivariatelocation AT yohaiv projectionestimatesofmultivariatelocation |
| _version_ |
1807316762458324992 |