A Rademacher-Menchov approach for random coefficient bifurcating autoregressive processes

TL;DR

This paper studies the asymptotic properties of estimators in random coefficient bifurcating autoregressive processes, establishing convergence, laws, and distributional results using martingale techniques and the Rademacher-Menchov theorem.

Contribution

It introduces a novel approach combining martingale asymptotics with the Rademacher-Menchov theorem to analyze estimators in bifurcating autoregressive models.

Findings

Almost sure convergence of estimators

Quadratic strong law established

Central limit theorems proved

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.