Convergence rates of kernel density estimators for stationary time series are well studied. For invertible linear processes, we construct a new density estimator that converges, in the supremum norm, at the better, parametric, rate n−1/2. Our estimator is a convolution of two different residual-based kernel estimators. We obtain in particular convergence rates for such residual-based kernel estimators; these results are of independent interest.
Publié le : 2007-04-14
Classification:
Least squares estimator,
kernel estimator,
plug-in estimator,
functional limit theorem,
infinite-order moving average process,
infinite-order autoregressive process,
62G07,
62G20,
62M05,
62M10
@article{1183667295,
author = {Schick, Anton and Wefelmeyer, Wolfgang},
title = {Uniformly root-n consistent density estimators for weakly dependent invertible linear processes},
journal = {Ann. Statist.},
volume = {35},
number = {1},
year = {2007},
pages = { 815-843},
language = {en},
url = {http://dml.mathdoc.fr/item/1183667295}
}
Schick, Anton; Wefelmeyer, Wolfgang. Uniformly root-n consistent density estimators for weakly dependent invertible linear processes. Ann. Statist., Tome 35 (2007) no. 1, pp. 815-843. http://gdmltest.u-ga.fr/item/1183667295/