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

Abstract

This study examines the bias in weighted least absolute deviation (WL1) 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 WL1 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 WL1 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 WL1 estimators, with their performance being particularly pronounced at the extremes of the autoregressive parameter range.