On the Berry-Esseen Bound for $L$-Statistics in the Non-I.D. Case with Applications to the Estimation of Location Parameters
Xiang, Xiaojing
Ann. Statist., Tome 22 (1994) no. 1, p. 968-979 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
In this paper, two versions of the Berry-Esseen theorems are established for $L$-statistics in the non-identically distributed case. One theorem, which requires $E|X_i|^3 < \infty$, is an extension of the classical Berry-Esseen theorem. Another, proved under the condition $E|X_i|^\alpha < \infty$ for some $\alpha \in (0, 1\rbrack$, seems to be of more interest for statistical inference. Some applications are also discussed.
Publié le : 1994-06-14
Classification:  $L$-statistics,  Berry-Esseen bound,  estimation of location parameter from non-i.d. sample,  60F05,  62F12,  62G30 
@article{1176325506,
     author = {Xiang, Xiaojing},
     title = {On the Berry-Esseen Bound for $L$-Statistics in the Non-I.D. Case with Applications to the Estimation of Location Parameters},
     journal = {Ann. Statist.},
     volume = {22},
     number = {1},
     year = {1994},
     pages = { 968-979},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176325506}
}

Xiang, Xiaojing. On the Berry-Esseen Bound for $L$-Statistics in the Non-I.D. Case with Applications to the Estimation of Location Parameters. Ann. Statist., Tome 22 (1994) no. 1, pp.  968-979. http://gdmltest.u-ga.fr/item/1176325506/