國立成功大學 統計學系

Standard sliced-based Sufficient Dimension Reduction (SDR) methods typically rely on reducing data slices to single point-valued summary statistics, such as conditional means, variances, or quantiles, thereby discarding significant structural information regarding the shape and support of the conditional distribution. To address this limitation, we propose Sliced Inverse Interval Estimation (SIIE), a novel framework that reimagines the slicing procedure through the lens of Symbolic Data Analysis (SDA). Instead of compressing slices into points, SIIE aggregates them into interval-valued hypercubes, preserving the topological support of the high-dimensional covariates. We construct a new symbolic kernel matrix based on these intervals and prove that its column space recovers the central subspace under mild conditions. We further establish that the estimator achieves root-n consistency and is computationally efficient. Extensive simulations and real data analyses demonstrate that SIIE is highly competitive with existing inverse moment-based methods, frequently offering superior performance in detecting symmetric dependencies and heteroscedasticity. Furthermore, it exhibits enhanced robustness against high-leverage outliers and data contamination compared to traditional approaches.