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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-10-01
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| Series: | Stats |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2571-905X/7/4/76 |
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| Summary: | 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. |
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| ISSN: | 2571-905X |