Model selection for generalized linear models with weak factors

The literature has witnessed an upsurge of interest in model selection in diverse fields and optimization applications. Despite the substantial progress, model selection remains a significant challenge when covariates are highly correlated, particularly within economic and financial datasets that exhibit cross-sectional and serial dependency. In this paper, we introduce a novel methodology named factor augmented regularized model selection with weak factors (WeakFARM) for generalized linear models in the presence of correlated covariates with weak latent factor structure. By identifying weak latent factors and idiosyncratic components and employing them as predictors, WeakFARM converts the challenge from model selection with highly correlated covariates to that with weakly correlated ones. Furthermore, we develop a variable screening method based on the proposed WeakFARM method. Comprehensive theoretical guarantees including estimation consistency, model selection consistency and sure screening property are also provided. We demonstrate the effectiveness of our approach by extensive simulation studies and a real data application in economic forecasting.