In this article, we propose and study the class of multivariate log-normal/independent distributions and linear regression models based on this class. The class of multivariate log-normal/independent distributions is very attractive for robust statistical modeling because it includes several heavy-tailed distributions suitable for modeling correlated multivariate positive data that are skewed and possibly heavy-tailed. Besides, expectation-maximization (EM)-type algorithms can be easily implemented for maximum likelihood estimation. We model the relationship between quantiles of the response variables and a set of explanatory variables, compute the maximum likelihood estimates of parameters through EM-type algorithms, and evaluate the model fitting based on Mahalanobis-type distances. The satisfactory performance of the quantile estimation is verified by simulation studies. An application to newborn data is presented and discussed.

中文翻译：

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通过多元对数正态/独立线性回归模型对新生儿数据进行分位数建模

在本文中，我们提出并研究了基于该类的多元对数正态/独立分布和线性回归模型的类。多元对数正态/独立分布类别对于稳健的统计建模非常有吸引力，因为它包括几个重尾分布，适用于对偏斜且可能是重尾的相关多元正数据进行建模。此外，对于最大似然估计，可以轻松实现期望最大化 (EM) 类型的算法。我们对响应变量的分位数与一组解释变量之间的关系进行建模，通过 EM 型算法计算参数的最大似然估计，并基于 Mahalanobis 型距离评估模型拟合。模拟研究验证了分位数估计的令人满意的性能。介绍并讨论了新生儿数据的应用。