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Abstract:

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.

Registro:

Documento: Artículo
Título:Projection estimates of multivariate location
Autor:Adrover, J.; Yohai, V.
Filiación:Fac. de Matemat. Astron./Fis., Univ. Nacional de Córdoba, Ciudad Universitaria, Avda. Medina Allende/Haya Torre, 5000 Córdoba, Argentina
Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellón 1, 1428 Buenos Aires, Argentina
Palabras clave:Maximum bias; Multivariate location; Projection estimates; Robust estimates
Año:2002
Volumen:30
Número:6
Página de inicio:1760
Página de fin:1781
DOI: http://dx.doi.org/10.1214/aos/1043351256
Título revista:Annals of Statistics
Título revista abreviado:Ann. Stat.
ISSN:00905364
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00905364_v30_n6_p1760_Adrover

Referencias:

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Citas:

---------- APA ----------
Adrover, J. & Yohai, V. (2002) . Projection estimates of multivariate location. Annals of Statistics, 30(6), 1760-1781.
http://dx.doi.org/10.1214/aos/1043351256
---------- CHICAGO ----------
Adrover, J., Yohai, V. "Projection estimates of multivariate location" . Annals of Statistics 30, no. 6 (2002) : 1760-1781.
http://dx.doi.org/10.1214/aos/1043351256
---------- MLA ----------
Adrover, J., Yohai, V. "Projection estimates of multivariate location" . Annals of Statistics, vol. 30, no. 6, 2002, pp. 1760-1781.
http://dx.doi.org/10.1214/aos/1043351256
---------- VANCOUVER ----------
Adrover, J., Yohai, V. Projection estimates of multivariate location. Ann. Stat. 2002;30(6):1760-1781.
http://dx.doi.org/10.1214/aos/1043351256