Estimators Related to $U$-Processes with Applications to Multivariate Medians: Asymptotic Normality
Arcones, Miguel A. ; Chen, Zhiqiang ; Gine, Evarist
Ann. Statist., Tome 22 (1994) no. 1, p. 1460-1477 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
If a criterion function $g(x_1, \ldots, x_m; \theta)$ depends on $m > 1$ samples, then a natural estimator of $\arg \max P^mg(x_1, \ldots, x_m; \theta)$ is the $\arg \max$ of a $U$-process. It is observed that, under suitable conditions, these estimators are asymptotically normal. This is then applied to prove asymptotic normality of Liu's simplical median and of Oja's medians in $\mathbb{R}^d$.
Publié le : 1994-09-14
Classification:  $M$-estimators,  $U$-processes,  Liu's simplicial median,  Oja's medians,  62F12,  62E20 
@article{1176325637,
     author = {Arcones, Miguel A. and Chen, Zhiqiang and Gine, Evarist},
     title = {Estimators Related to $U$-Processes with Applications to Multivariate Medians: Asymptotic Normality},
     journal = {Ann. Statist.},
     volume = {22},
     number = {1},
     year = {1994},
     pages = { 1460-1477},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176325637}
}

Arcones, Miguel A.; Chen, Zhiqiang; Gine, Evarist. Estimators Related to $U$-Processes with Applications to Multivariate Medians: Asymptotic Normality. Ann. Statist., Tome 22 (1994) no. 1, pp.  1460-1477. http://gdmltest.u-ga.fr/item/1176325637/