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

41 pagesInternational audienceThe 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

Deviation inequalities and moderate deviations for estimators of parameters in 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 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. 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. MSC: 60F10; 62F12; 60G42; 62M10; 62G0

Moderate deviations for the mildly stationary autoregressive models with dependent errors

In this paper, we consider the normalized least squares estimator of the parameter in a mildly stationary first-order autoregressive model with dependent errors which are modeled as a mildly stationary AR(1) process. By martingale methods, we establish the moderate deviations for the least squares estimators of the regressor and error, which can be applied to understand the near-integrated second order autoregressive processes. As an application, we obtain the moderate deviations for the Durbin-Watson statistic.Comment: Comments welcome. 28 page

Transportation cost-information and concentration inequalities for bifurcating Markov chains

We investigate the transportation cost-information inequalities for bifurcating Markov chains which are a class of processes indexed by binary tree. These processes provide models for cell growth when each individual in one generation gives birth to two offsprings in the next one. Transportation cost inequalities provide useful concentra-tion inequalities. We also study deviation inequalities for the empiri-cal means under relaxed assumptions on the Wasserstein contraction of the Markov kernels. Applications to bifurcating non linear autore-gressive processes are considered: deviation inequalities for pointwise estimates of the non linear leading functions