A Rademacher-Menchov approach for random coefficient bifurcating autoregressive processes

Bernard Bercu (1, 2) , Vassili Blandin (1, 2)

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

We investigate the asymptotic behavior of the least squares estimator of the unknown parameters of random coefficient bifurcating autoregressive processes. Under suitable assumptions on inherited and environmental effects, we establish the almost sure convergence of our estimates. In addition, we also prove a quadratic strong law and central limit theorems. Our approach mainly relies on asymptotic results for vector-valued martingales together with the well-known Rademacher-Menchov theorem.

Domains: Probability [math.PR]; Statistics Theory [stat.TH]

Bernard Bercu, Vassili Blandin. A Rademacher-Menchov approach for random coefficient bifurcating autoregressive processes. 2012. ⟨hal-00745634⟩