Ensemble Conditional Variance Estimation for Sufficient Dimension Reduction

Abstract

Conditional Variance Estimation (CVE) and Ensemble Conditional Variance Estimation (ECVE) are novel sufficient dimension reduction (SDR) methods in regressions with continuous response and predictors. Conditional Variance Estimation applies to additive error regressions with continuous predictors and link function and ECVE to general non-additive error regression models. Both operate under the assumption that the predictors can be replaced by a lower dimensional projection without loss of information. They are semiparametric forward regression model-based exhaustive sufficient dimension reduction estimation methods that are shown to be consistent under mild assumptions. CVE outperforms mean average variance estimation (MAVE) and ECVE outperforms central subspace mean average variance estimation (csMAVE), their main competitors, under several simulation settings and in benchmark data set analyses.