On the Asymptotic Distribution of a Weighted Least Absolute Deviation Estimate for a Bifurcating Autoregressive Process

This paper introduces a new class of estimates for estimating the parameter vector of a first-order bifurcating autoregressive model. The estimates minimize a sum of weighted absolute deviations where the weights are of the Schweppe variety. Asymptotic linearity properties are derived for the so called WL1-estimate. Based on these properties, the WL1-estimate is shown to be asymptotically normal at rate n(1/2). The results hinge on two new law of large numbers theorems for bifurcating processes. As an application of the theory, some asymptotic relative efficiency comparisons are made.