The purpose of this paper is to investigate moderate deviations for the Durbin-Watson statistic associated with the stable first-order autoregressive process where the driven noise is also given by a first-order autoregressive process. We first establish a moderate deviation principle for both the least squares estimator of the unknown parameter of the autoregressive process as well as for the serial correlation estimator associated with the driven noise. It enables us to provide a moderate deviation principle for the Durbin-Watson statistic in the case where the driven noise is normally distributed and in the more general case where the driven noise satisfies a less restrictive Chen-Ledoux type condition.
Mots clés : Durbin-Watson statistic, moderate deviation principle, first-order autoregressive process, serial correlation
@article{PS_2014__18__308_0,
author = {Bitseki Penda, S. Val\`ere and Djellout, Hac\`ene and Pro{\"\i}a, Fr\'ed\'eric},
title = {Moderate deviations for the {Durbin-Watson} statistic related to the first-order autoregressive process},
journal = {ESAIM: Probability and Statistics},
pages = {308--331},
publisher = {EDP-Sciences},
volume = {18},
year = {2014},
doi = {10.1051/ps/2013038},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2013038/}
}
TY - JOUR AU - Bitseki Penda, S. Valère AU - Djellout, Hacène AU - Proïa, Frédéric TI - Moderate deviations for the Durbin-Watson statistic related to the first-order autoregressive process JO - ESAIM: Probability and Statistics PY - 2014 SP - 308 EP - 331 VL - 18 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2013038/ DO - 10.1051/ps/2013038 LA - en ID - PS_2014__18__308_0 ER -
%0 Journal Article %A Bitseki Penda, S. Valère %A Djellout, Hacène %A Proïa, Frédéric %T Moderate deviations for the Durbin-Watson statistic related to the first-order autoregressive process %J ESAIM: Probability and Statistics %D 2014 %P 308-331 %V 18 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2013038/ %R 10.1051/ps/2013038 %G en %F PS_2014__18__308_0
Bitseki Penda, S. Valère; Djellout, Hacène; Proïa, Frédéric. Moderate deviations for the Durbin-Watson statistic related to the first-order autoregressive process. ESAIM: Probability and Statistics, Tome 18 (2014), pp. 308-331. doi : 10.1051/ps/2013038. http://www.numdam.org/articles/10.1051/ps/2013038/
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