A1229
Title: High-dimensional regression: Model averaging and inference
Authors: Lise Leonard - UCLouvain (Belgium) [presenting]
Eugen Pircalabelu - Université catholique de Louvain (Belgium)
Rainer von Sachs - UC Louvain (Belgium)
Abstract: With the advent of technology and the proliferation of data collection methods, researchers now have access to vast amounts of data. High-dimensional regression models are designed to handle datasets with more predictors than observations. However, these methods, such as the Lasso, depend on unknown tuning parameters. A procedure for high-dimensional model averaging is proposed that allows inference, with the goal of eliminating the difficult choice of the tuning parameter and obtaining an asymptotically Gaussian estimator. The main feature of the procedure is to pool together information from multiple estimators to obtain a single, final estimator. A strategy based on the debiased Lasso estimator is proposed to aggregate regression coefficients to reduce the prediction risk of the estimation and to eliminate the influence of the tuning parameter. Theoretical results on the distribution and the prediction risk of the method are presented. In particular, the asymptotic normality of the estimator is shown even after the aggregation and the optimality of the prediction loss. The performance of the method is illustrated through numerical simulations and an application on a real, high-dimensional dataset.
