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Abstract : 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 a quadratic strong law and central limit theorems. All our investigation relies on asymptotic results for vector-valued martingales.

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

Author: Bernard Bercu - Vassili Blandin -



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