ABSTRACT Multivariate regression analysis studies relationships between more than one response variables and predictor variables. Traditionally, observation values are assumed to be precise numbers while in many life-like situations data are collected in an imprecise way and contain some outliers inevitably. Characterizing imprecise observations as uncertain variables, this paper gives a novel least absolute deviations estimator for the unknown parameter in uncertain multivariate regression model, which is more robust to outliers compared with the least-squares estimator and more suitable in life-like situations. In addition, residual analysis, prediction values and prediction intervals for response variables with new imprecise predictor variables are presented. Finally, numerical examples and simulation with real traffic data illustrate the robustness of our method with outliers in imprecise observations.

中文翻译：

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不确定多元回归模型的最小绝对偏差

摘要 多元回归分析研究不止一个响应变量和预测变量之间的关系。传统上，观察值被假定为精确的数字，而在许多栩栩如生的情况下，数据的收集方式并不精确，并且不可避免地包含一些异常值。将不精确的观测表征为不确定变量，本文针对不确定多元回归模型中的未知参数给出了一种新颖的最小绝对偏差估计量，与最小二乘估计量相比，它对异常值的鲁棒性更强，更适用于栩栩如生的情况。此外，还介绍了具有新的不精确预测变量的响应变量的残差分析、预测值和预测区间。最后，