Expectile regression neural network model with applications

The expectile regression neural network (ERNN) model is proposed.It is flexible and can be used to explore potential nonlinear effects of covariates.It is a general model that incorporates several popular models as specials cases.It can be estimated through standard gradient based optimization algorithms.It outputs conditional expectile functions directly. Recently, nonlinear expectile regression becomes popular because it can not only explore nonlinear relationships among variables, but also describe the complete distribution of a response variable conditional on covariates information. In contrast, the traditional nonlinear expectile regression mainly confronts two shortcomings. First, it is difficult to select an appropriate form of nonlinear function. Second, it ignores the interaction effects among covariates. In this paper, we develop a new expectile regression neural network (ERNN) model by adding a neural network structure to expectile regression approach. The proposed ERNN model is flexible and can be used to explore potential nonlinear effects of covariates on expectiles of the response. The ERNN model can be easily estimated through standard gradient based optimization algorithms and output conditional expectile functions directly. The advantage of ERNN model is illustrated by Monte Carlo simulation studies. The numerical results show that the ERNN model outperforms the conventional expectile regression and support vector machine models in terms of predictive ability with both in-sample and out-of-sample test. We also apply the ERNN model to the predictions of concrete compressive strength and housing price. It turns out the marginal contribution of each predictor to the conditional expectile of a response is useful for decision-making.