Robust Total Least Squares Estimation Method for Uncertain Linear Regression Model

In data analysis and modeling, least squares and total least squares are both mathematical optimization techniques. It is noteworthy that both the least squares method and the total least squares method are used to deal with precise and random data. However, when the given data are not random, or when the data are imprecise, and only the range of the data is available, the traditional linear regression method cannot be used. This paper presents an uncertain total least squares estimation method and an uncertain robust total least squares linear regression method based on uncertainty theory and total least squares method. The uncertain total least squares estimation can fully consider errors in the given data and the uncertain robust total least squares linear regression method can effectively eliminate outliers in the data. It is possible to obtain a more reasonable fitting effect with both of these methods, as well as to solve the predicted value and the confidence interval with these two methods. In terms of robust total least squares linear regression estimation, both uncertain total least squares regression estimation and uncertain robust total least squares regression estimation are feasible based on numerical examples. There are more accurate fitting equations and more reliable results with uncertain robust least squares linear regression estimation.