Prediction in abundant high-dimensional linear regression

Abstract

An abundant regression is one in which most of the predictors contribute information about the response, which is contrary to the common notion of a sparse regression where few of the predictors are relevant. We discuss asymptotic characteristics of methodology for prediction in abundant linear regressions as the sample size and number of predictors increase in various alignments. We show that some of the estimators can perform well for the purpose of prediction in abundant high-dimensional regressions.