Bias Analysis and Correction in Weighted- L 1 Estimators for the First-Order Bifurcating Autoregressive Model

Tamer Elbayoumi () and Sayed Mostafa
Additional contact information
Tamer Elbayoumi: 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

Stats, 2024, vol. 7, issue 4, 1-18

Abstract: This study examines the bias in weighted least absolute deviation ( W L 1 ) 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 W L 1 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 W L 1 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 W L 1 estimators, with their performance being particularly pronounced at the extremes of the autoregressive parameter range.

Keywords: bifurcating; autoregressive; singe bootstrap; fast double bootstrap (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2571-905X/7/4/76/pdf (application/pdf)
https://www.mdpi.com/2571-905X/7/4/76/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jstats:v:7:y:2024:i:4:p:76-1332:d:1510736

Access Statistics for this article

Stats is currently edited by Mrs. Minnie Li

More articles in Stats from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().