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Journal Articles ESAIM: Probability and Statistics Year : 2014

Random coefficients bifurcating autoregressive processes

Abstract

This paper presents a new model of asymmetric bifurcating autoregressive process with random coefficients. We couple this model with a Galton Watson tree to take into account possibly missing observations. We propose least-squares estimators for the various parameters of the model and prove their consistency, with a convergence rate, and asymptotic normality. We use both the bifurcating Markov chain and martingale approaches and derive new important general results in both these frameworks.

Dates and versions

hal-00702357 , version 1 (30-05-2012)

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Benoîte de Saporta, Anne Gégout-Petit, Laurence Marsalle. Random coefficients bifurcating autoregressive processes. ESAIM: Probability and Statistics, 2014, 18, pp.365-399. ⟨10.1051/ps/2013042⟩. ⟨hal-00702357⟩
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