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Multivariate linear regression with non-normal errors: a solution based on mixture models

机译：具有非正态误差的多元线性回归：基于混合模型的解决方案

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摘要

In some situations, the distribution of the error terms of a multivariate linear regression model may depart from normality. This problem has been addressed, for example, by specifying a different parametric distribution family for the error terms, such as multivariate skewed and/or heavy-tailed distributions. A new solution is proposed, which is obtained by modelling the error term distribution through a finite mixture of multi-dimensional Gaussian components. The multivariate linear regression model is studied under this assumption. Identifiability conditions are proved and maximum likelihood estimation of the model parameters is performed using the EM algorithm. The number of mixture components is chosen through model selection criteria; when this number is equal to one, the proposal results in the classical approach. The performances of the proposed approach are evaluated through Monte Carlo experiments and compared to the ones of other approaches. In conclusion, the results obtained from the analysis of a real dataset are presented.
机译：在某些情况下，多元线性回归模型的误差项的分布可能会偏离正态性。例如，通过为误差项指定不同的参数分布族（例如多元偏斜分布和/或重尾分布）来解决此问题。提出了一种新的解决方案，该解决方案是通过对多维高斯分量的有限混合进行误差项分布建模而获得的。在此假设下研究了多元线性回归模型。证明了可识别性条件，并使用EM算法对模型参数进行了最大似然估计。通过模型选择标准选择混合物成分的数量；当此数字等于1时，该建议采用经典方法。通过蒙特卡洛实验评估了所提出方法的性能，并与其他方法进行了比较。总之，介绍了从真实数据集的分析中获得的结果。

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