The semiparametric varying-coefficient composite expectile regression model in risk measurement and its application

We propose a class of semiparametric composite expectile models with varying-coefficients via combining a semiparametric regression model with varying-coefficients, the EVaR thought and the assumption that using all information from multiple expectiles can improve the efficient of estimators. In this paper, we introduce estimation called composite expectile regression (CER), and we establish large sample properties of the resulting CER estimator. Based on the fact that the model includes the parametric part and the nonparametric part, we adopt a three-step estimating procedure. Our simulation studies demonstrate that our CER estimator is competent to the existing estimators, e.g. the least squares (LS) estimator or other expectile regression (ER) estimators, in the sense of root mean squared-error when the error follows a heavy-tailed or asymmetric distribution. In addition, we use the proposed method to analyze the relationship between China's monetary policy and Shanghai Composite Index.