We consider the problem of estimating a functional of a density of the type $\int \phi (f, \cdot)$. Starting from efficient estimators of linear and quadratic functionals of f and using a Taylor expansion of $\phi$,
we build estimators that achieve the $n^{-1/2}$ rate whenever f is smooth enough. Moreover, we show that these estimators are efficient. Concerning the estimation of quadratic functionals (more precisely, of integrated squared density) Bickel and Ritov have already built efficient estimators. We propose here an alternative construction based on projections, which seems more natural.
Publié le : 1996-04-14
Classification:
Estimation of density,
projection methods,
kernel estimators,
Fourier series,
semiparametric Cramér-Rao bound,
62G06,
62G07,
62G20
@article{1032894458,
author = {Laurent, B\'eatrice},
title = {Efficient estimation of integral functionals of a density},
journal = {Ann. Statist.},
volume = {24},
number = {6},
year = {1996},
pages = { 659-681},
language = {en},
url = {http://dml.mathdoc.fr/item/1032894458}
}
Laurent, Béatrice. Efficient estimation of integral functionals of a density. Ann. Statist., Tome 24 (1996) no. 6, pp. 659-681. http://gdmltest.u-ga.fr/item/1032894458/