A Robust Approach to CCRM Interval Regression considering Interval Coincidence Degree

Abstract

Traditional CCRMs (Constrained Center-and-Range Methods) in solving the problem of interval regression could hardly make tradeoffs between the overall fitting accuracy and the coincidence degree between the observed and predicted intervals and could also hardly reduce the number of disjoint elements between the observed and predicted intervals, as well as raise the average ratio of all predicted intervals contained within their observed intervals. This paper constructed a nonlinear regression model based on center-and-range method, in which the maximization of coincidence degree for the sample with the worst coincidence degree between the observed and predicted interval was incorporated into the traditional CCRM model’s objective. This novel nonlinear programming model was proven to be a convex one that satisfied K-T condition. Monte Carlo simulation shows that the model is degenerated to the compared CCRM+ model as the objective only contains the minimization of the overall fitting accuracy for both center and range sample series. In this situation, it could obtain a better solution than the use of the compared CCRM model. In addition, when the proposed model only takes into account the maximization of coincidence degree for the sample with the worst coincidence degree between the observed and predicted interval, the model shows a better performance than the CCRM+ model in terms of the average ratio of all predicted intervals contained within their observed intervals, as well as the average number of forecasts with 0% accuracy.