IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i4p932-d1066003.html
   My bibliography  Save this article

Bias-Corrected Inference of High-Dimensional Generalized Linear Models

Author

Listed:
  • Shengfei Tang

    (School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China)

  • Yanmei Shi

    (School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China)

  • Qi Zhang

    (School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China)

Abstract

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.

Suggested Citation

  • Shengfei Tang & Yanmei Shi & Qi Zhang, 2023. "Bias-Corrected Inference of High-Dimensional Generalized Linear Models," Mathematics, MDPI, vol. 11(4), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:932-:d:1066003
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/4/932/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/4/932/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yinchu Zhu & Jelena Bradic, 2018. "Linear Hypothesis Testing in Dense High-Dimensional Linear Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(524), pages 1583-1600, October.
    2. Song, Yunquan & Liang, Xijun & Zhu, Yanji & Lin, Lu, 2021. "Robust variable selection with exponential squared loss for the spatial autoregressive model," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    3. Alexandre Belloni & Victor Chernozhukov & Ying Wei, 2016. "Post-Selection Inference for Generalized Linear Models With Many Controls," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 606-619, October.
    4. Yunlu Jiang & Yan Wang & Jiantao Zhang & Baojian Xie & Jibiao Liao & Wenhui Liao, 2021. "Outlier detection and robust variable selection via the penalized weighted LAD-LASSO method," Journal of Applied Statistics, Taylor & Francis Journals, vol. 48(2), pages 234-246, January.
    5. Alex K. Shalek & Rahul Satija & Joe Shuga & John J. Trombetta & Dave Gennert & Diana Lu & Peilin Chen & Rona S. Gertner & Jellert T. Gaublomme & Nir Yosef & Schraga Schwartz & Brian Fowler & Suzanne W, 2014. "Single-cell RNA-seq reveals dynamic paracrine control of cellular variation," Nature, Nature, vol. 510(7505), pages 363-369, June.
    6. Ortega, Edwin M. M. & Bolfarine, Heleno & Paula, Gilberto A., 2003. "Influence diagnostics in generalized log-gamma regression models," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 165-186, February.
    7. Adel Javanmard & Jason D. Lee, 2020. "A flexible framework for hypothesis testing in high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 685-718, July.
    8. Faming Liang & Jingnan Xue & Bochao Jia, 2022. "Markov Neighborhood Regression for High-Dimensional Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(539), pages 1200-1214, September.
    9. Chengchun Shi & Rui Song & Wenbin Lu & Runze Li, 2021. "Statistical Inference for High-Dimensional Models via Recursive Online-Score Estimation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(535), pages 1307-1318, July.
    10. Ryoya Oda & Yoshie Mima & Hirokazu Yanagihara & Yasunori Fujikoshi, 2021. "A high-dimensional bias-corrected AIC for selecting response variables in multivariate calibration," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(14), pages 3453-3476, July.
    11. Rong Ma & T. Tony Cai & Hongzhe Li, 2021. "Global and Simultaneous Hypothesis Testing for High-Dimensional Logistic Regression Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(534), pages 984-998, April.
    12. Susan Athey & Guido W. Imbens & Stefan Wager, 2018. "Approximate residual balancing: debiased inference of average treatment effects in high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(4), pages 597-623, September.
    13. Tianxi Cai & T. Tony Cai & Zijian Guo, 2021. "Optimal statistical inference for individualized treatment effects in high‐dimensional models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(4), pages 669-719, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tianxi Cai & T. Tony Cai & Zijian Guo, 2021. "Optimal statistical inference for individualized treatment effects in high‐dimensional models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(4), pages 669-719, September.
    2. Harold D. Chiang, 2018. "Many Average Partial Effects: with An Application to Text Regression," Papers 1812.09397, arXiv.org, revised Jan 2022.
    3. Jelena Bradic & Stefan Wager & Yinchu Zhu, 2019. "Sparsity Double Robust Inference of Average Treatment Effects," Papers 1905.00744, arXiv.org.
    4. Masahiro Kato, 2024. "Triple/Debiased Lasso for Statistical Inference of Conditional Average Treatment Effects," Papers 2403.03240, arXiv.org.
    5. Lechner, Michael, 2018. "Modified Causal Forests for Estimating Heterogeneous Causal Effects," IZA Discussion Papers 12040, Institute of Labor Economics (IZA).
    6. Alexandre Belloni & Victor Chernozhukov & Denis Chetverikov & Christian Hansen & Kengo Kato, 2018. "High-dimensional econometrics and regularized GMM," CeMMAP working papers CWP35/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Kyle Colangelo & Ying-Ying Lee, 2019. "Double debiased machine learning nonparametric inference with continuous treatments," CeMMAP working papers CWP72/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Jelena Bradic & Weijie Ji & Yuqian Zhang, 2021. "High-dimensional Inference for Dynamic Treatment Effects," Papers 2110.04924, arXiv.org, revised May 2023.
    9. Davide Viviano & Jelena Bradic, 2019. "Synthetic learner: model-free inference on treatments over time," Papers 1904.01490, arXiv.org, revised Aug 2022.
    10. Sung Jae Jun & Sokbae Lee, 2024. "Causal Inference Under Outcome-Based Sampling with Monotonicity Assumptions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(3), pages 998-1009, July.
    11. Sylvie Rato & Antonio Rausell & Miguel Muñoz & Amalio Telenti & Angela Ciuffi, 2017. "Single-cell analysis identifies cellular markers of the HIV permissive cell," PLOS Pathogens, Public Library of Science, vol. 13(10), pages 1-23, October.
    12. Jiaxuan Liang & Yi Cheng & Yuqi Su & Shuyue Xiao & Yunquan Song, 2022. "Variable Selection for Spatial Logistic Autoregressive Models," Mathematics, MDPI, vol. 10(17), pages 1-16, August.
    13. Michael C. Knaus, 2021. "A double machine learning approach to estimate the effects of musical practice on student’s skills," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(1), pages 282-300, January.
    14. Croux, Christophe & Jagtiani, Julapa & Korivi, Tarunsai & Vulanovic, Milos, 2020. "Important factors determining Fintech loan default: Evidence from a lendingclub consumer platform," Journal of Economic Behavior & Organization, Elsevier, vol. 173(C), pages 270-296.
    15. Kyle Colangelo & Ying-Ying Lee, 2019. "Double debiased machine learning nonparametric inference with continuous treatments," CeMMAP working papers CWP54/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    16. Chunrong Ai & Oliver Linton & Kaiji Motegi & Zheng Zhang, 2021. "A unified framework for efficient estimation of general treatment models," Quantitative Economics, Econometric Society, vol. 12(3), pages 779-816, July.
    17. Victor Chernozhukov & Whitney K. Newey & Victor Quintas-Martinez & Vasilis Syrgkanis, 2021. "Automatic Debiased Machine Learning via Riesz Regression," Papers 2104.14737, arXiv.org, revised Mar 2024.
    18. Benjamin Lu & Eli Ben-Michael & Avi Feller & Luke Miratrix, 2023. "Is It Who You Are or Where You Are? Accounting for Compositional Differences in Cross-Site Treatment Effect Variation," Journal of Educational and Behavioral Statistics, , vol. 48(4), pages 420-453, August.
    19. Undral Byambadalai, 2022. "Identification and Inference for Welfare Gains without Unconfoundedness," Papers 2207.04314, arXiv.org.
    20. Sviták, Jan & Tichem, Jan & Haasbeek, Stefan, 2021. "Price effects of search advertising restrictions," International Journal of Industrial Organization, Elsevier, vol. 77(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:932-:d:1066003. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.