An Alternative Regularity Condition for Hajek's Representation Theorem
Tierney, Luke
Ann. Statist., Tome 15 (1987) no. 1, p. 427-431 / Harvested from Project Euclid
Hajek's representation theorem states that under certain regularity conditions the limiting distribution of an estimator can be written as the convolution of a certain normal distribution with some other distribution. This result, originally developed for finite dimensional problems, has been extended to a number of infinite dimensional settings where it has been used, for example, to establish the asymptotic efficiency of the Kaplan-Meier estimator. The purpose of this note is to show that the somewhat unintuitive regularity condition on the estimators that is usually used can be replaced by a simple one: It is sufficient for the asymptotic information and the limiting distribution of the estimator to vary continuously with the parameter being estimated.
Publié le : 1987-03-14
Classification:  Asymptotic efficiency,  regular estimators,  62G20,  62G05
@article{1176350277,
     author = {Tierney, Luke},
     title = {An Alternative Regularity Condition for Hajek's Representation Theorem},
     journal = {Ann. Statist.},
     volume = {15},
     number = {1},
     year = {1987},
     pages = { 427-431},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176350277}
}
Tierney, Luke. An Alternative Regularity Condition for Hajek's Representation Theorem. Ann. Statist., Tome 15 (1987) no. 1, pp.  427-431. http://gdmltest.u-ga.fr/item/1176350277/