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 and 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. ECVE outperforms central subspace mean average variance estimation (csMAVE), its main competitor, under several simulation settings and in a benchmark data set analysis.
Funding Statement
L. Fertl was supported by Austrian Science Fund (FWF P 30690-N35). E. Bura was supported by Austrian Science Fund (FWF P 30690-N35) and Vienna Science and Technology Fund (WWTF ICT19-018)
Acknowledgments
The authors thank Daniel Kapla for his programming assistance. Daniel Kapla also co-authored the CVE R package that implements the proposed method.
Citation
Lukas Fertl. Efstathia Bura. "The ensemble conditional variance estimator for sufficient dimension reduction." Electron. J. Statist. 16 (1) 1595 - 1634, 2022. https://doi.org/10.1214/22-EJS1994