Multivariate data is collected in many fields, such as chemometrics, econometrics, financial engineering and genetics. In multivariate data, heteroscedasticity and collinearity occur frequently. And selecting material predictors is also a key issue when analyzing multivariate data. To accomplish these tasks, multivariate linear regression model is often constructed. We thus propose row-sparse elastic-net regularized multivariate Huber regression model in this paper. For this new model, we proof its grouping effect property and the property of resisting sample outliers. Based on the KKT condition, an accelerated proximal sub-gradient algorithm is designed to solve the proposed model and its convergency is also established. To demonstrate the accuracy and efficiency, simulation and real data experiments are carried out. The numerical results show that the new model can deal with heteroscedasticity and collinearity well.

多元数据收集于许多领域，例如化学计量学，计量经济学，金融工程学和遗传学。在多元数据中，经常出现异方差和共线性。分析多元数据时，选择重要的预测指标也是关键问题。为了完成这些任务，通常构建多元线性回归模型。因此，我们在本文中提出行稀疏弹性网正则化多元Huber回归模型。对于这个新模型，我们证明了其分组效果属性和抵抗样本离群值的属性。基于KKT条件，设计了一种加速的近梯度子梯度算法来求解该模型，并建立了算法的收敛性。为了证明准确性和效率，进行了仿真和真实数据实验。