Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

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

S. Valère Bitseki Penda and Hacène Djellout

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Abstract

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.

Résumé

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.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 50, Number 3 (2014), 806-844.

Dates
First available in Project Euclid: 20 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1403276999

Digital Object Identifier
doi:10.1214/13-AIHP545

Mathematical Reviews number (MathSciNet)
MR3224290

Zentralblatt MATH identifier
1302.60052

Subjects
Primary: 60F10: Large deviations 62F12: Asymptotic properties of estimators 60G42: Martingales with discrete parameter 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62G05: Estimation

Keywords
Deviation inequalities Moderate deviation principle Bifurcating autoregressive process Martingale Limit theorems Least squares estimation

Citation

Bitseki Penda, S. Valère; Djellout, Hacène. Deviation inequalities and moderate deviations for estimators of parameters in bifurcating autoregressive models. Ann. Inst. H. Poincaré Probab. Statist. 50 (2014), no. 3, 806--844. doi:10.1214/13-AIHP545. https://projecteuclid.org/euclid.aihp/1403276999


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