Weighted L1-estimates for the First-order Bifurcating Autoregressive Model

We developed robust estimators that minimize a weighted L1 norm for the first-order bifurcating autoregressive model. When all of the weights are fixed, our estimate is an L1 estimate that is robust against outlying points in the response space and more efficient than the least squares estimate for heavy-tailed error distributions. When the weights are random and depend on the points in the factor space, the weighted L1 estimate is robust against outlying points in the factor space. Simulated and artificial examples are presented. The behavior of the proposed estimate is modeled through a Monte Carlo study.