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 n1/2. 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.