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

A Rademacher-Menchov approach for random coefficient bifurcating autoregressive processes