Least absolute deviations uncertain regression with imprecise observations

Abstract: Traditionally regression analysis answers questions about the relationships among variables based on the assumption that the observation values of variables are precise numbers. It has long been dominated by least squares techniques, mostly due to their elegant theoretical foundation and ease of implementation. However, in many cases, we can only get imprecise observation values and the assumptions upon which the least squares is based may not be valid. So this paper characterizes the imprecise data in terms of uncertain variables and proposes a novel robust approach under the principle of least absolute deviations to estimate the unknown parameters in uncertain regression models. Finally, numerical examples are documented to illustrate our method.