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 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.

Automated summary

In this paper, a weighted link-specific (WLS) approach is proposed for high-dimensional Poisson and Gamma regression, providing a unified statistical inference framework. By regressing the parameter deviations and initial estimation errors, the resulting regression coefficients are utilized as correction weights to decrease the total mean square error (MSE). Additionally, the asymptotic normality of the correction estimates is developed under sparse and non-sparse conditions, and associated confidence intervals (CIs) are constructed to verify the robustness of the new method. Numerical simulations and empirical analysis demonstrate the extensive and effective nature of the WLS method.