Generalized Ridge Estimators in High-Dimensional Generalized Linear Models

Abstract

The paper presents a generalized ridge approach for high dimensional generalized linear models where dimensionality exceeds sample size. When the vector of covariate coefficient paraters β is sparse, a thresholding method for high dimensional generalized linear models is presented, enabling simultaneous variable selection and parameter estimation without the uniform signal strength assumption. Theoretical guarantees for variable selection and estimation, including consistency and convergence rates, are derived under some regularity conditions. Simulation studies and a real world data analysis are conducted to examine the performance of the proposed approach.