Moment-Based Adjustments of Statistical Inference in High-Dimensional Generalized Linear Models

Understand

We develop a statistical inference method for generalized linear models (GLMs) in high-dimensional settings, where the number of unknown coefficients $p$ is of the same order as the sample size $n$.

• In this regime, constructing confidence intervals requires estimating unknown hyperparameters, such as the signal strength.
• However, existing estimators for the hyperparameters are not stably applicable to GLMs when $p/n$ is close to or greater than $1$, both theoretically and empirically.
• In this study, we develop an estimator for the hyperparameter that addresses the issue and establish an inferential framework, provided that the link function of the GLM exhibits an asymmetry property.