Deviation inequalities and moderate deviations for estimators of parameters in bifurcating autoregressive models

Bitseki Penda, S. Valère; Djellout, Hacène

Annales de l'I.H.P. Probabilités et statistiques, Tome 50 (2014) no. 3, pp. 806-844.

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.

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 $p$th-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.

Classification : 60F10, 62F12, 60G42, 62M10, 62G05
Mots clés : deviation inequalities, moderate deviation principle, bifurcating autoregressive process, martingale, limit theorems, least squares estimation

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