Bootstrap Methods for Correcting Bias in WLS Estimators of the First-Order Bifurcating Autoregressive Model

Tamer Elbayoumi (), Mutiyat Usman, Sayed Mostafa, Mohammad Zayed and Ahmad Aboalkhair
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Tamer Elbayoumi: Department of Mathematics and Statistics, North Carolina A&T State University, 1601 E. Market Street, Greensboro, NC 27411, USA
Mutiyat Usman: Department of Mathematics and Statistics, North Carolina A&T State University, 1601 E. Market Street, Greensboro, NC 27411, USA
Sayed Mostafa: Department of Mathematics and Statistics, North Carolina A&T State University, 1601 E. Market Street, Greensboro, NC 27411, USA
Mohammad Zayed: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh 11623, Saudi Arabia
Ahmad Aboalkhair: Department of Applied Statistics and Insurance, Faculty of Commerce, Mansoura University, El Gomhouria St., El Mansoura 1, Dakahlia Governorate 35516, Egypt

Stats, 2025, vol. 8, issue 3, 1-23

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.

Keywords: bifurcating; autoregressive; weighted LS; single bootstrap; fast double bootstrap; shrinking approach (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:gam:jstats:v:8:y:2025:i:3:p:79-:d:1743511

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