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E. Bura, L. Fertl:
"Conditional Variance Estimator for Sufficient Dimension Reduction";
Bernoulli, 28 (2022), 3; 1862 - 1891.

Conditional Variance Estimation (CVE) is a novel sufficient dimension reduction (SDR) method for additive error
regressions with continuous predictors and link function. It operates under the assumption that the predictors can
be replaced by a lower dimensional projection without loss of information. Conditional Variance Estimation is
fully data driven, does not require the restrictive linearity and constant variance conditions, and is not based on
inverse regression as the majority of moment and likelihood based sufficient dimension reduction methods. CVE is
shown to be consistent and its objective function to be uniformly convergent. CVE outperforms the mean average
variance estimation, (MAVE), its main competitor, in several simulation settings, remains on par under others,
while it always outperforms inverse regression based linear SDR methods, such as Sliced Inverse Regression.

Regression; Nonparametric; Mean subspace; Minimum average variance estimation; Dimension reduction

http://dx.doi.org/10.3150/21-BEJ1402