Conditional Variance Estimator for Sufficient Dimension Reduction

TL;DR

Conditional Variance Estimation (CVE) is a new data-driven method for sufficient dimension reduction in additive error regressions, avoiding restrictive assumptions and outperforming traditional inverse regression techniques in various simulations.

Contribution

CVE introduces a fully data-driven SDR approach that does not rely on linearity or constant variance assumptions, enhancing flexibility and performance.

Findings

CVE is consistent and has uniformly convergent objective function.

CVE outperforms MAVE in several simulation settings.

CVE always outperforms inverse regression based SDR methods like Sliced Inverse Regression.

Abstract

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.