We consider in this paper two widely studied examples of nonparametric and semiparametric models in which the standard information bounds are totally misleading. In fact, no estimators converge at the $n^{-\alpha}$ rate for any $\alpha > 0$, although the information is strictly positive "promising" that $n^{-1/2}$ is achievable. The examples are the estimation of $\int p^2$ and the slope in the model of Engle et al. A class of models in which the parameter of interest can be estimated efficiently is discussed.
Publié le : 1990-06-14
Classification:
Rate of convergence,
nonparametric estimations,
functionals of a density,
62G20,
62G05
@article{1176347633,
author = {Ritov, Y. and Bickel, P. J.},
title = {Achieving Information Bounds in Non and Semiparametric Models},
journal = {Ann. Statist.},
volume = {18},
number = {1},
year = {1990},
pages = { 925-938},
language = {en},
url = {http://dml.mathdoc.fr/item/1176347633}
}
Ritov, Y.; Bickel, P. J. Achieving Information Bounds in Non and Semiparametric Models. Ann. Statist., Tome 18 (1990) no. 1, pp. 925-938. http://gdmltest.u-ga.fr/item/1176347633/