Limit theorems for bifurcating integer-valued autoregressive processes

Vassili Blandin (1, 2)

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

We study the asymptotic behavior of the weighted least squares estimators of the unknown parameters of bifurcating integer-valued autoregressive processes. Under suitable assumptions on the immigration, we establish the almost sure convergence of our estimators, together with the quadratic strong law and central limit theorems. All our investigation relies on asymptotic results for vector-valued martingales.

Mots clés: bifurcating autoregressive process; integer-valued process; weighted least squares; martingale; almost sure convergence; central limit theorem

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

Vassili Blandin. Limit theorems for bifurcating integer-valued autoregressive processes. 2012. ⟨hal-00696297⟩