Faculty Candidate for Assistant Professor in Statistics

Abstract:

The envelope model provides substantial efficiency gains over the standard multivariate linear regression by identifying the material part of the response to the model and by excluding the immaterial part. In this talk, we propose the enhanced response envelope by incorporating a novel envelope regularization term in its formulation. It is shown that the enhanced response envelope can yield better prediction risk than the original envelope estimator. The enhanced response envelope naturally handles high-dimensional data. In an asymptotic high-dimensional regime where the ratio of the number of predictors over the number of samples converges to a non-zero constant, we reveal an interesting double descent phenomenon for the first time for the envelope model. A simulation study confirms our main theoretical findings. Simulations and real data applications demonstrate that the enhanced response envelope does have significantly improved prediction performance over the original envelope estimator.