The desire to make nonparametric regression robust leads to the problem of conditional median function estimation. Under appropriate regularity conditions, a sequence of local median estimators can be chosen to achieve the optimal rate of convergence $n^{-1/(2+d)}$ both pointwise and in the $L^q (1 \leq q < \infty)$ norm restricted to a compact. It can also be chosen to achieve the optimal rate of convergence $(n^{-1} \log n)^{1/(2+d)}$ in the $L^\infty$ norm restricted to a compact. These results also constitute an answer to an open question of Stone.
Publié le : 1989-06-14
Classification:
Kernel estimator,
nonparametric regression,
conditional median function,
local median,
rate of convergence,
62G05,
62E20
@article{1176347128,
author = {Truong, Young K.},
title = {Asymptotic Properties of Kernel Estimators Based on Local Medians},
journal = {Ann. Statist.},
volume = {17},
number = {1},
year = {1989},
pages = { 606-617},
language = {en},
url = {http://dml.mathdoc.fr/item/1176347128}
}
Truong, Young K. Asymptotic Properties of Kernel Estimators Based on Local Medians. Ann. Statist., Tome 17 (1989) no. 1, pp. 606-617. http://gdmltest.u-ga.fr/item/1176347128/