Title: Efficient estimation in expectile regression using envelope models
Authors: Zhihua Su - University of Florida (United States) [presenting]
Shanshan Ding - University of Delaware (United States)
Yi Yang - McGill University (Canada)
Tuo Chen - University of Florida (United States)
Abstract: Expectile is an important risk measure with unique advantages and wide applications in the fields of econometrics and finance. The expectile regression (ER) with respect to different expectile levels can provide a comprehensive picture of the conditional distribution of the response variable given the predictors. We adopt an efficient estimation method called the envelope model in ER, and construct a novel envelope expectile regression (EER). Estimation of the EER parameters can be performed using the generalized method of moments (GMM). We establish the consistency and derive the asymptotic distribution of the EER estimators. In addition, we show that the EER estimators are asymptotically more efficient than the ER estimators. Numerical experiments and real data examples are provided to demonstrate the efficiency gains attained by EER compared to ER, and the efficiency gains can further lead to advantages in prediction.