Let $(\mathbf{X}_t, Y_t)$ be a stationary time series with $\mathbf{X}_t$ being $R^d$-valued and $Y_t$ real valued, and where $Y_t$ is not necessarily bounded. Let $E(Y_0 \mid \mathbf{X}_0)$ be the conditional mean function. Under appropriate regularity conditions, local average estimators of this function can be chosen to achieve the optimal rate of convergence $(n^{-1} \log n)^{1/(d + 2)}$ in $L_\infty$ norm restricted to a compact. The result answers a question raised by Truong and Stone.
Publié le : 1993-06-14
Classification:
Nonparametric estimation,
strong mixing,
local mean,
62G07,
62G05,
62G20
@article{1176349163,
author = {Tran, Lanh Tat},
title = {Nonparametric Function Estimation for Time Series by Local Average Estimators},
journal = {Ann. Statist.},
volume = {21},
number = {1},
year = {1993},
pages = { 1040-1057},
language = {en},
url = {http://dml.mathdoc.fr/item/1176349163}
}
Tran, Lanh Tat. Nonparametric Function Estimation for Time Series by Local Average Estimators. Ann. Statist., Tome 21 (1993) no. 1, pp. 1040-1057. http://gdmltest.u-ga.fr/item/1176349163/