Composite quantile regression neural network with applications

Abstract

In recent years, there has been growing interest in neural network to explore complex patterns. We consider an extension of this framework in composite quantile regression setup and propose a novel composite quantile regression neural network (CQRNN) model. We further construct a differential approximation to the quantile regression loss function, and develop an estimation procedure using standard gradient-based optimization algorithms. The CQRNN model is flexible and efficient to explore potential nonlinear relationships among variables, which we demonstrate both in Monte Carlo simulation studies and three real-world applications. It enhances the nonlinear processing capacity of ANN and enables us to achieve desired results for handling different types of data. In addition, our method also provides an idea to bridge the gap between composite quantile regression and intelligent methods such as ANNs, SVM, etc., which is helpful to improve their robustness, goodness-of-fit and predictive ability.