Bias-Corrected Inference of High-Dimensional Generalized Linear Models
In this paper, we propose a weighted link-specific (WLS) approach that establishes a unified statistical inference framework for high-dimensional Poisson and Gamma regression. We regress the parameter deviations as well as the initial estimation errors and utilize the resulting regression coefficien...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/4/932 |
| _version_ | 1797619552892223488 |
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| author | Shengfei Tang Yanmei Shi Qi Zhang |
| author_facet | Shengfei Tang Yanmei Shi Qi Zhang |
| author_sort | Shengfei Tang |
| collection | DOAJ |
| description | In this paper, we propose a weighted link-specific (WLS) approach that establishes a unified statistical inference framework for high-dimensional Poisson and Gamma regression. We regress the parameter deviations as well as the initial estimation errors and utilize the resulting regression coefficients as correction weights to reduce the total mean square error (MSE). We also develop the asymptotic normality of the correction estimates under sparse and non-sparse conditions and construct associated confidence intervals (CIs) to verify the robustness of the new method. Finally, numerical simulations and empirical analysis show that the WLS method is extensive and effective. |
| first_indexed | 2024-03-11T08:28:38Z |
| format | Article |
| id | doaj.art-b753c853485d4c73a42005b806645e9d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T08:28:38Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b753c853485d4c73a42005b806645e9d2023-11-16T21:56:01ZengMDPI AGMathematics2227-73902023-02-0111493210.3390/math11040932Bias-Corrected Inference of High-Dimensional Generalized Linear ModelsShengfei Tang0Yanmei Shi1Qi Zhang2School of Mathematics and Statistics, Qingdao University, Qingdao 266071, ChinaSchool of Mathematics and Statistics, Qingdao University, Qingdao 266071, ChinaSchool of Mathematics and Statistics, Qingdao University, Qingdao 266071, ChinaIn this paper, we propose a weighted link-specific (WLS) approach that establishes a unified statistical inference framework for high-dimensional Poisson and Gamma regression. We regress the parameter deviations as well as the initial estimation errors and utilize the resulting regression coefficients as correction weights to reduce the total mean square error (MSE). We also develop the asymptotic normality of the correction estimates under sparse and non-sparse conditions and construct associated confidence intervals (CIs) to verify the robustness of the new method. Finally, numerical simulations and empirical analysis show that the WLS method is extensive and effective.https://www.mdpi.com/2227-7390/11/4/932generalized linear modelmean square errorbias-correctionlink-specific |
| spellingShingle | Shengfei Tang Yanmei Shi Qi Zhang Bias-Corrected Inference of High-Dimensional Generalized Linear Models Mathematics generalized linear model mean square error bias-correction link-specific |
| title | Bias-Corrected Inference of High-Dimensional Generalized Linear Models |
| title_full | Bias-Corrected Inference of High-Dimensional Generalized Linear Models |
| title_fullStr | Bias-Corrected Inference of High-Dimensional Generalized Linear Models |
| title_full_unstemmed | Bias-Corrected Inference of High-Dimensional Generalized Linear Models |
| title_short | Bias-Corrected Inference of High-Dimensional Generalized Linear Models |
| title_sort | bias corrected inference of high dimensional generalized linear models |
| topic | generalized linear model mean square error bias-correction link-specific |
| url | https://www.mdpi.com/2227-7390/11/4/932 |
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