  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. In contrast to the majority of moment based sufficient dimension
reduction methods, Conditional Variance Estimation is fully data driven, does
not require the restrictive linearity and constant variance conditions, and is
not based on inverse regression. 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 the usual
inverse regression based linear SDR methods, such as Sliced Inverse Regression.
