Bias Analysis and Correction in Weighted-L1 Estimators for the First-Order Bifurcating Autoregressive Model

This study examines the bias in weighted least absolute deviation ( (Formula presented.) ) estimation within the context of stationary first-order bifurcating autoregressive (BAR(1)) models, which are frequently employed to analyze binary tree-like data, including applications in cell lineage studies. Initial findings indicate that (Formula presented.) estimators can demonstrate substantial and problematic biases, especially when small to moderate sample sizes. The autoregressive parameter and the correlation between model errors influence the volume and direction of the bias. To address this issue, we propose two bootstrap-based bias-corrected estimators for the (Formula presented.) estimator. We conduct extensive simulations to assess the performance of these bias-corrected estimators. Our empirical findings demonstrate that these estimators effectively reduce the bias inherent in (Formula presented.) estimators, with their performance being particularly pronounced at the extremes of the autoregressive parameter range.