Uncertain least squares estimation model based on relative error

Abstract

Uncertain least squares estimation is one of the important methods to deal with imprecise data, which can fully consider the influence of given data on regression equation and minimize the absolute error. In fact, some scientific studies or observational data are often evaluated in terms of relative error, which to some extent allows the error of the forecasting value to vary with the size of the observed value. Based on the least squares estimation and the uncertainty theory, this paper proposed the uncertain relative error least squares estimation model of the linear regression. The uncertain relative error least squares estimation minimizes the relative error, which can not only solve the fitting regression equation of the imprecise observation data, but also fully consider the variation of the error with the given data, so the regression equation is more reasonable and reliable. Two numerical examples verified the feasibility of the uncertain relative error least squares estimation, and compared it with the existing method. The data analysis shows that the uncertain relative error least squares estimation has a good fitting effect.