Ensemble Conditional Variance Estimator for Sufficient Dimension Reduction

TL;DR

This paper introduces ECVE, a new semiparametric method for sufficient dimension reduction in regression models with continuous responses, demonstrating superior performance over existing methods in simulations and real data.

Contribution

The paper proposes ECVE, a novel ensemble-based SDR method applicable to non-additive error models, with proven consistency and improved accuracy over csMAVE.

Findings

ECVE outperforms csMAVE in simulations.

ECVE is consistent under mild assumptions.

ECVE effectively reduces dimensionality in benchmark data.

Abstract

Ensemble Conditional Variance Estimation (ECVE) is a novel sufficient dimension reduction (SDR) method in regressions with continuous response and predictors. ECVE applies to general non-additive error regression models. It operates under the assumption that the predictors can be replaced by a lower dimensional projection without loss of information. It is a semiparametric forward regression model based exhaustive sufficient dimension reduction estimation method that is shown to be consistent under mild assumptions. It is shown to outperform central subspace mean average variance estimation (csMAVE), its main competitor, under several simulation settings and in a benchmark data set analysis.