Variable Screening and Model Averaging for Expectile Regressions
针对分位数回归提出分位数相关和偏相关概念，用于超高维变量筛选，并建议用扩展贝叶斯信息准则和刀切模型平均处理模型不确定性，理论证明其有效性。
Expectile regression is a useful tool in modelling data with heterogeneous conditional distributions. This paper introduces two new concepts, i.e. the expectile correlation and expectile partial correlation, which can measure the contribution from each regressor to the response in expectile regression. In ultra‐high dimensional setting, the expectile partial correlation, which provides an importance ranking of the predictors, is found useful for variable screening. Theoretical results indicate that the proposed screening procedure can achieve the sure screening set. Additionally, a model selection method via extended Bayesian information criterion (EBIC) and a jackknife model averaging (JMA) method are suggested after the screening step to address model uncertainty. The screening consistency of EBIC, the asymptotic optimality of JMA in the sense of minimizing out‐of‐sample expectile final prediction error, and the sparsity of JMA weight are then established. Finally, numerical results demonstrate the nice performance of our proposed methods.