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, mostly due to the 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. Furthermore, some general estimate approaches are also explored. Finally, numerical examples illustrate that our estimate is more robust than the least squares implying it is more suitable to handle observations with outliers.

中文翻译：

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用不精确的观测值进行不确定回归的最小绝对偏差估计

传统上，回归分析基于变量的观察值是精确数字的假设来回答有关变量之间关系的问题。长期以来，它一直以最小二乘为主，这主要是由于其优雅的理论基础和易于实现的功能。但是，在许多情况下，我们只能获得不精确的观测值，并且最小二乘方所基于的假设可能无效。因此，本文根据不确定变量来表征不精确数据，并提出了一种基于最小绝对偏差原理的鲁棒方法，用于估计不确定回归模型中的未知参数。此外，还探索了一些通用的估计方法。最后，