Estimating sufficient reductions of the predictors in abundant high-dimensional regressions

TL;DR

This paper analyzes the asymptotic properties of sufficient dimension reduction methods in high-dimensional regressions, demonstrating their consistency and oracle rates in abundant predictor settings through theoretical and simulation results.

Contribution

It provides a theoretical framework for the consistency of dimension reduction methods in high-dimensional, abundant predictor scenarios, supported by simulations.

Findings

Methods are consistent in various high-dimensional settings.

Oracle rates are achievable in abundant regressions.

Simulation results confirm theoretical predictions.

Abstract

We study the asymptotic behavior of a class of methods for sufficient dimension reduction in high-dimension regressions, as the sample size and number of predictors grow in various alignments. It is demonstrated that these methods are consistent in a variety of settings, particularly in abundant regressions where most predictors contribute some information on the response, and oracle rates are possible. Simulation results are presented to support the theoretical conclusion.