Uncertain regression model based on Huber loss function

Abstract

In classic regression analysis, both the explanatory variables and response variables of the study are assumed to be exact data. However, in practical cases, we find some observations to be imprecise. Therefore, we regard the observed data as uncertain variables, and study the functional relationship between variables through uncertain regression analysis under the uncertainty theory. In this paper, we first propose Huber estimation based on the Huber loss function about uncertain regression model, which can effectively reduce the influence of outliers on the analysis results. Second, we put forward leave-one-out cross-validation method to select and adjust the unknown parameter in the Huber loss function. Then, a real numerical example illustrates the feasibility of Huber estimation. Finally, two simulated experimental examples are used to verify effectiveness of the estimation method for influence of outliers by comparing least squares and least absolute deviation.