A0174
Title: Robust estimation of central subspace under high-dimensional and elliptical-contoured design
Authors: Jing Zeng - University of Science and Technology of China (China) [presenting]
Qing Mai - Florida State University (United States)
Abstract: Sufficient dimension reduction (SDR) is a valuable tool to tackle high dimensionality while maintaining the primary information of the prediction problem, and it has demonstrated great promise in many applications. There exists a variety of high-dimensional sufficient dimension reduction methods in the literature. However, they all rely on the sub-Gaussian assumption of the predictors' marginal distribution or conditional distribution. Such a light-tailedness assumption is frequently violated in real life. A new methodology is proposed to estimate the central subspace consistently when the predictor exhibits heavy-tailedness. The novel proposal overcomes the heavy-tailedness issue and the high dimensionality. Under a general regression model assumption and the elliptically-contoured distribution assumption of the predictor, an invariance result between the CS and a surrogate subspace is established. TEstimatingthe surrogate subspace avoids the heavy-tailedness issue and can be implemented using existing high-dimensional SDR methods. Theoretically, the proposal enjoys satisfactory consistency, and the convergence rate is shown to achieve optimality. Empirically, the efficiency and effectiveness of the recommendation are demonstrated by extensive simulation studies and real data examples.
