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

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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)

  • Sayed Mostafa

    (Department of Mathematics and Statistics, North Carolina A&T State University, 1601 E. Market Street, Greensboro, NC 27411, USA)

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.

Suggested Citation

  • Tamer Elbayoumi & Sayed Mostafa, 2024. "Bias Analysis and Correction in Weighted- L 1 Estimators for the First-Order Bifurcating Autoregressive Model," Stats, MDPI, vol. 7(4), pages 1-18, October.
    • Handle: RePEc:gam:jstats:v:7:y:2024:i:4:p:76-1332:d:1510736
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    References listed on IDEAS

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    1. K. D. Patterson, 2007. "Bias Reduction through First-order Mean Correction, Bootstrapping and Recursive Mean Adjustment," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(1), pages 23-45.
    2. Shi, Sheng G., 1992. "Accurate and efficient double-bootstrap confidence limit method," Computational Statistics & Data Analysis, Elsevier, vol. 13(1), pages 21-32, January.
    3. Hisashi Tanizaki & Shigeyuki Hamori & Yoichi Matsubayashi, 2006. "On least-squares bias in the AR(p) models: Bias correction using the bootstrap methods," Statistical Papers, Springer, vol. 47(1), pages 109-124, January.
    4. MacKinnon, James G. & Smith Jr., Anthony A., 1998. "Approximate bias correction in econometrics," Journal of Econometrics, Elsevier, vol. 85(2), pages 205-230, August.
    5. Oded Sandler & Sivan Pearl Mizrahi & Noga Weiss & Oded Agam & Itamar Simon & Nathalie Q. Balaban, 2015. "Lineage correlations of single cell division time as a probe of cell-cycle dynamics," Nature, Nature, vol. 519(7544), pages 468-471, March.
    6. Jinyuan Chang & Peter Hall, 2015. "Double-bootstrap methods that use a single double-bootstrap simulation," Biometrika, Biometrika Trust, vol. 102(1), pages 203-214.
    7. Jeremy Berkowitz & Lutz Kilian, 2000. "Recent developments in bootstrapping time series," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 1-48.
    8. S. M. S. Lee & G. A. Young, 1999. "The effect of Monte Carlo approximation on coverage error of double‐bootstrap confidence intervals," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 353-366, April.
    9. Zhou, J. & Basawa, I.V., 2005. "Least-squares estimation for bifurcating autoregressive processes," Statistics & Probability Letters, Elsevier, vol. 74(1), pages 77-88, August.
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