Post-Shrinkage Strategies in High-dimensional Generalized Linear Models

• Brock Universit, St. Catharines, Canada [sahmed5@brocku.ca]

Keywords: Generalized Linear Model; High-dimensional Data; Shrinkage estimation; Weak signals

In this talk we present post-shrinkage strategies for high-dimensional generalized linear models in the presence of weak signals. For high-dimensional data (HDD) many penalized methods were introduced for simultaneous variable selection and parameters estimation when the model is sparse. However, a model may have sparse signals as well as many predictors with weak signals. In this scenario, variable selection methods may not distinguish predictors with weak signals and sparse signals. For this reason, we propose a high-dimensional post-shrinkage strategy to improve the prediction performance of a generalized linear submodel. We establish that the proposed post-shrinkage strategy performs better than the penalized and machine learning methods in many cases. Some asymptotic results are established, and extensive numerical experiments are conducted to evaluate the performance of our proposed post-shrinkage strategy. These numerical results demonstrate the effectiveness of our strategy and corroborate the theoretical results. Furthermore, we illustrate the application of our strategy with high-dimensional data. Finally, I will also discuss some new research problems with possible partial solutions.