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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
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