In statistical applications the unknown parameter of interest can frequently be defined as a functional $\theta=T(F)$, where F is an unknown population. Statistical inferences about $\theta$ are usually made based on the statistic $T(F_n)$, where $F_n$ is the empirical distribution. Assessing $T(F_n)$ (as an estimator of $\theta$) or making large sample inferences usually requires a consistent estimator of the asymptotic variance of $T(F_n)$. Asymptotic behavior of the jackknife variance estimator is closely related to the smoothness of the functional T. This paper studies the smoothness of T through the differentiability of T and establishes some general results for the consistency of the jackknife variance estimators. The results are applied to some examples in which the statistics $T(F_n)$ are L-, M-estimators and some test statistics.
Publié le : 1993-03-14
Classification:
Gateaux derivative,
Frechet differentiability,
continuous differentiability,
L-estimators,
M-estimators,
linear rank statistics,
variance estimation,
62G05,
62E99
@article{1176349015,
author = {Shao, Jun},
title = {Differentiability of Statistical Functionals and Consistency of the Jackknife},
journal = {Ann. Statist.},
volume = {21},
number = {1},
year = {1993},
pages = { 61-75},
language = {en},
url = {http://dml.mathdoc.fr/item/1176349015}
}
Shao, Jun. Differentiability of Statistical Functionals and Consistency of the Jackknife. Ann. Statist., Tome 21 (1993) no. 1, pp. 61-75. http://gdmltest.u-ga.fr/item/1176349015/