Bootstrap Methods for Correcting Bias in WLS Estimators of the First-Order Bifurcating Autoregressive Model
Year: 2025
Type: article
Abstract: In this study, we examine the presence of bias in weighted least squares (WLS) estimation within the context of first-order bifurcating autoregressive (BAR(1)) models. These models are widely used in the analysis of binary tree-structured data, particularly in cell lineage research. Our findings suggest that WLS estimators may exhibit significant and problematic biases, especially in finite samples. The magnitude and direction of this bias are influenced by both the autoregressive parameter and the correlation structure of the model errors. To address this issue, we propose two bootstrap-based methods for bias correction of the WLS estimator. The paper further introduces shrinkage-based versions of both single and fast double bootstrap bias correction techniques, designed to mitigate the over-correction and under-correction issues that may arise with traditional bootstrap methods, particularly in larger samples. Comprehensive simulation studies were conducted to evaluate the performance of the proposed bias-corrected estimators. The results show that the proposed corrections substantially reduce bias, with the most notable improvements observed at extreme values of the autoregressive parameter. Moreover, the study provides practical guidance for practitioners on method selection under varying conditions.
Source: Stats
DOI: 10.3390/stats8030079
Authors: Tamer Elbayoumi, Mutiyat Usman, Sayed Mostafa, Mohammad Zayed, Ahmad Aboalkhair
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,930
OpenAlex ID: W4414013357