Dimension reduction with expectation of conditional difference measure

In this article, we introduce a flexible model-free approach to sufficient dimension reduction analysis using the expectation of conditional difference measure. Without any strict conditions, such as linearity condition or constant covariance condition, the method estimates the central subspace exhaustively and efficiently under linear or nonlinear relationships between response and predictors. The method is especially meaningful when the response is categorical. We also studied the $ \sqrt {n} $ n-consistency and asymptotic normality of the estimate. The efficacy of our method is demonstrated through both simulations and a real data analysis.