Local asymptotic normality for bifurcating autoregressive processes and related asymptotic inference

Abstract

This article is concerned with the local asymptotic normality (LAN) of the log-likelihood for the bifurcating autoregressive model (BAR) for tree structured data where each individual in one generation gives rise to two off-spring in the next generation. We derive the LAN property for the p th-order BAR model. Asymptotic optimal inference for the model parameters can be deduced as a consequence of LAN. In particular, an efficient score test is derived as an application. A simulation study is conducted to address the issue regarding how many generations are required for asymptotic results to be useful in practice.