Open Access
2022 The ensemble conditional variance estimator for sufficient dimension reduction
Lukas Fertl, Efstathia Bura
Author Affiliations +
Electron. J. Statist. 16(1): 1595-1634 (2022). DOI: 10.1214/22-EJS1994


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)


The authors thank Daniel Kapla for his programming assistance. Daniel Kapla also co-authored the CVE R package that implements the proposed method.


Download Citation

Lukas Fertl. Efstathia Bura. "The ensemble conditional variance estimator for sufficient dimension reduction." Electron. J. Statist. 16 (1) 1595 - 1634, 2022.


Received: 1 March 2021; Published: 2022
First available in Project Euclid: 7 March 2022

MathSciNet: MR4390504
zbMATH: 07524959
Digital Object Identifier: 10.1214/22-EJS1994

Keywords: central subspace , ensembles , linear sufficient reduction , regression , semi-parametric

Vol.16 • No. 1 • 2022
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