Tukey's biweight estimation for uncertain regression model with imprecise observations

The purpose of regression analysis is to study how a response variable has a relation to a vector of explanatory variables. Traditionally, statisticians assume that the observation data are precise, and we can get some exact values. However, in many cases, the imprecise observation data are available. We assume that these data are uncertain variables in the sense of uncertainty theory. In this paper, the Tukey biweight or bisquare family of loss functions is applied to estimate unknown parameters satisfying the uncertain regression model. First, the Tukey biweight estimations of three types of regression models are given, namely linear, asymptotic and Michaelis-Menten. Then an empirical study is presented to verify the feasibility of this approach. Finally, the effectiveness of this method in weakening the outliers influence is shown by the comparative analysis.