Deviation inequalities and moderate deviations for estimators of parameters in bifurcating autoregressive models
Annales de l'I.H.P. Probabilités et statistiques, Volume 50 (2014) no. 3, p. 806-844

The purpose of this paper is to investigate the deviation inequalities and the moderate deviation principle of the least squares estimators of the unknown parameters of general pth-order asymmetric bifurcating autoregressive processes, under suitable assumptions on the driven noise of the process. Our investigation relies on the moderate deviation principle for martingales.

L’objetcif de ce papier est d’établir des inégalités de déviations et les principes de déviations modérées pour les estimateurs des moindres carrés des paramètres inconnus d’un processus bifurcant autorégressif asymétrique d’ordre p, sous certaines conditions sur la suite des bruits. Les preuves reposent sur les principes de déviations modérées des martingales.

DOI : https://doi.org/10.1214/13-AIHP545
Classification:  60F10,  62F12,  60G42,  62M10,  62G05
Keywords: deviation inequalities, moderate deviation principle, bifurcating autoregressive process, martingale, limit theorems, least squares estimation
@article{AIHPB_2014__50_3_806_0,
     author = {Bitseki Penda, S. Val\`ere and Djellout, Hac\`ene},
     title = {Deviation inequalities and moderate deviations for estimators of parameters in bifurcating autoregressive models},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {50},
     number = {3},
     year = {2014},
     pages = {806-844},
     doi = {10.1214/13-AIHP545},
     zbl = {1302.60052},
     mrnumber = {3224290},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2014__50_3_806_0}
}
Bitseki Penda, S. Valère; Djellout, Hacène. Deviation inequalities and moderate deviations for estimators of parameters in bifurcating autoregressive models. Annales de l'I.H.P. Probabilités et statistiques, Volume 50 (2014) no. 3, pp. 806-844. doi : 10.1214/13-AIHP545. http://www.numdam.org/item/AIHPB_2014__50_3_806_0/

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