A Rademacher-Menchov approach for random coefficient bifurcating autoregressive processes

Bernard Bercu 1, 2 Vassili Blandin 1, 2
2 ALEA - Advanced Learning Evolutionary Algorithms
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5251
Abstract : 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.
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https://hal.inria.fr/hal-00745634
Contributor : Vassili Blandin <>
Submitted on : Friday, October 26, 2012 - 9:24:08 AM
Last modification on : Thursday, January 11, 2018 - 6:22:36 AM

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  • HAL Id : hal-00745634, version 1
  • ARXIV : 1210.5835

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

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