Bias Analysis and Correction in Weighted-<i>L</i><sub>1</sub> Estimators for the First-Order Bifurcating Autoregressive Model
This study examines the bias in weighted least absolute deviation (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="normal">W</mi><msub><mi>L</mi><...
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2024-10-01
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| author | Tamer Elbayoumi Sayed Mostafa |
| author_facet | Tamer Elbayoumi Sayed Mostafa |
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| description | This study examines the bias in weighted least absolute deviation (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="normal">W</mi><msub><mi>L</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula>) 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="normal">W</mi><msub><mi>L</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="normal">W</mi><msub><mi>L</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="normal">W</mi><msub><mi>L</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> estimators, with their performance being particularly pronounced at the extremes of the autoregressive parameter range. |
| format | Article |
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| language | English |
| publishDate | 2024-10-01 |
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| series | Stats |
| spelling | doaj-art-c0c6d40353fa4759be242d2d5e333acf2025-08-20T02:01:24ZengMDPI AGStats2571-905X2024-10-01741315133210.3390/stats7040076Bias Analysis and Correction in Weighted-<i>L</i><sub>1</sub> Estimators for the First-Order Bifurcating Autoregressive ModelTamer Elbayoumi0Sayed Mostafa1Department of Mathematics and Statistics, North Carolina A&T State University, 1601 E. Market Street, Greensboro, NC 27411, USADepartment of Mathematics and Statistics, North Carolina A&T State University, 1601 E. Market Street, Greensboro, NC 27411, USAThis study examines the bias in weighted least absolute deviation (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="normal">W</mi><msub><mi>L</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula>) 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="normal">W</mi><msub><mi>L</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="normal">W</mi><msub><mi>L</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="normal">W</mi><msub><mi>L</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> estimators, with their performance being particularly pronounced at the extremes of the autoregressive parameter range.https://www.mdpi.com/2571-905X/7/4/76bifurcatingautoregressivesinge bootstrapfast double bootstrap |
| spellingShingle | Tamer Elbayoumi Sayed Mostafa Bias Analysis and Correction in Weighted-<i>L</i><sub>1</sub> Estimators for the First-Order Bifurcating Autoregressive Model Stats bifurcating autoregressive singe bootstrap fast double bootstrap |
| title | Bias Analysis and Correction in Weighted-<i>L</i><sub>1</sub> Estimators for the First-Order Bifurcating Autoregressive Model |
| title_full | Bias Analysis and Correction in Weighted-<i>L</i><sub>1</sub> Estimators for the First-Order Bifurcating Autoregressive Model |
| title_fullStr | Bias Analysis and Correction in Weighted-<i>L</i><sub>1</sub> Estimators for the First-Order Bifurcating Autoregressive Model |
| title_full_unstemmed | Bias Analysis and Correction in Weighted-<i>L</i><sub>1</sub> Estimators for the First-Order Bifurcating Autoregressive Model |
| title_short | Bias Analysis and Correction in Weighted-<i>L</i><sub>1</sub> Estimators for the First-Order Bifurcating Autoregressive Model |
| title_sort | bias analysis and correction in weighted i l i sub 1 sub estimators for the first order bifurcating autoregressive model |
| topic | bifurcating autoregressive singe bootstrap fast double bootstrap |
| url | https://www.mdpi.com/2571-905X/7/4/76 |
| work_keys_str_mv | AT tamerelbayoumi biasanalysisandcorrectioninweightedilisub1subestimatorsforthefirstorderbifurcatingautoregressivemodel AT sayedmostafa biasanalysisandcorrectioninweightedilisub1subestimatorsforthefirstorderbifurcatingautoregressivemodel |