In this paper we obtain root- consistency and functional central limit theorems in weighted -spaces for plug-in estimators of the two-step transition density in the classical stationary linear autoregressive model of order one, assuming essentially only that the innovation density has bounded variation. We also show that plugging in a properly weighted residual-based kernel estimator for the unknown innovation density improves on plugging in an unweighted residual-based kernel estimator. These weights are chosen to exploit the fact that the innovations have mean zero. If an efficient estimator for the autoregression parameter is used, then the weighted plug-in estimator for the two-step transition density is efficient. Our approach generalizes to invertible linear processes.
Mots-clés : empirical likelihood, Owen estimator, least dispersed regular estimator, efficient influence function, stochastic expansion of residual-based kernel density estimator
@article{PS_2009__13__135_0,
author = {Schick, Anton and Wefelmeyer, Wolfgang},
title = {Plug-in estimators for higher-order transition densities in autoregression},
journal = {ESAIM: Probability and Statistics},
pages = {135--151},
publisher = {EDP-Sciences},
volume = {13},
year = {2009},
doi = {10.1051/ps:2008001},
mrnumber = {2502027},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps:2008001/}
}
TY - JOUR AU - Schick, Anton AU - Wefelmeyer, Wolfgang TI - Plug-in estimators for higher-order transition densities in autoregression JO - ESAIM: Probability and Statistics PY - 2009 SP - 135 EP - 151 VL - 13 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps:2008001/ DO - 10.1051/ps:2008001 LA - en ID - PS_2009__13__135_0 ER -
%0 Journal Article %A Schick, Anton %A Wefelmeyer, Wolfgang %T Plug-in estimators for higher-order transition densities in autoregression %J ESAIM: Probability and Statistics %D 2009 %P 135-151 %V 13 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps:2008001/ %R 10.1051/ps:2008001 %G en %F PS_2009__13__135_0
Schick, Anton; Wefelmeyer, Wolfgang. Plug-in estimators for higher-order transition densities in autoregression. ESAIM: Probability and Statistics, Tome 13 (2009), pp. 135-151. doi : 10.1051/ps:2008001. http://archive.numdam.org/articles/10.1051/ps:2008001/
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