Least absolute deviations for uncertain multivariate regression model

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.