高维重尾数据下的切片逆Kendall's Tau估计

摘要

Sufficient dimension reduction is an important branch of statistical learning, which performs an optimal projection of covariates under a supervised learning framework. Most of the existing sufficient dimension reduction algorithms require strict restrictions on the distribution of models, making them sensitive to heavy-tailed predictors and outliers. In this article, we propose a novel method called Sliced Inverse Kendall’s tau Estimation (SIKE) designed for analyzing heavy-tailed, elliptically distributed and high-dimensional data that find wide application, especially in finance and economics. Compared with other existing methods, SIKE does not require computing median or conditional median, thus imposes milder conditions on the method and increases the precision of estimation. Furthermore, a remedial algorithm is introduced in discouraging situation, which enhances the general adaptability of our method. We investigate the theoretical properties of SIKE as the dimension p diverges with sample size n. Extensive simulation studies show that SIKE performs significantly well for various scenarios. Analyses of asset pricing data and housing data also demonstrate the effectiveness of our proposed method.