A0430
Title: Dimension reduction for extreme regression via contour projection
Authors: Liujun Chen - University of Science and Technology of China (China)
Jing Zeng - University of Science and Technology of China (China) [presenting]
Abstract: In the context of regression problems, a primary objective is to infer the extreme values of the response given a set of predictors. The high dimensionality and heavy-tailedness of predictors pose significant challenges, limiting the applicability of classical tools for inferring conditional extremes. The focus is on the central extreme subspace (CES), whose existence and uniqueness are guaranteed under fairly mild conditions. By projecting the data onto CES, the dimension of the predictors is reduced while all information for inferring conditional extremes is retained, which effectively addresses the high dimensionality issue. Then, the novel COPSE method is proposed to estimate CES, involving the projection of predictors onto an elliptical contour. Notably, COPES exhibits robustness against heavy-tailed data. The theoretical justification is provided for the consistency of COPES under mild assumptions. Overall, the proposal not only extends the toolkit for extreme regression but also broadens the scope of the dimension reduction techniques. The effectiveness of the proposal is demonstrated through extensive simulation studies and an application to Chinese stock market data.
