Asymptotic results for bifurcating random coefficient autoregressive processes

Vassili Blandin (1, 2)

1 ALEA - Advanced Learning Evolutionary Algorithms
2 IMB - Institut de Mathématiques de Bordeaux

The purpose of this paper is to study the asymptotic behavior of the weighted least square estimators of the unknown parameters of random coefficient bifurcating autoregressive processes. Under suitable assumptions on the immigration and the inheritance, we establish the almost sure convergence of our estimators, as well as a quadratic strong law and central limit theorems. Our study mostly relies on limit theorems for vector-valued martingales.

Mots clés: bifurcating autoregressive process; random coefficient; weighted least squares; martingale; almost sure convergence; central limit theorem

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Vassili Blandin. Asymptotic results for bifurcating random coefficient autoregressive processes. 2012. ⟨hal-00696295⟩