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

TL;DR

This paper studies deviation inequalities and moderate deviation principles for least squares estimators of parameters in bifurcating autoregressive models, using martingale techniques under certain noise assumptions.

Contribution

It introduces new deviation inequalities and moderate deviation results for estimators in bifurcating autoregressive processes, extending existing theoretical frameworks.

Findings

Established deviation inequalities for estimators.

Proved moderate deviation principles under specified conditions.

Applied martingale methods to bifurcating autoregressive models.

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 bifurcating autoregressive processes, under suitable assumptions on the driven noise of the process. Our investigation relies on the moderate deviation principle for martingales.