ABSTRACT This work presents a log-linear model for multivariate Birnbaum–Saunders distribution that can be used in survival analysis to investigate correlated log-lifetimes of two or more units. This model is studied through the use of a generalized multivariate sinh-normal distribution, which is built from the multivariate mixture scale of normal distributions. The marginal and conditional linear regression models of the proposed multivariate Birnbaum–Saunders linear regression model are generalizations of the Birnbaum–Saunders linear regression models of Rieck and Nedelman [A log-linear model for the Birnbaum-Saunders distribution. Technometrics. 1991;33:51–60], which have been used effectively to model lifetime and reliability data. We exploit a nice hierarchical representation of the regression model to propose a fast and accurate EM algorithm to compute the maximum likelihood estimates of the model parameters. Hypothesis testing is also performed by the use of the asymptotic normality of the maximum likelihood estimators. Finally, the results of simulation studies as well as an application to a real dataset are displayed, where we also is include a robustness feature of the estimation procedure developed here.

中文翻译：

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稳健的多变量 Birnbaum-Saunders 回归模型

摘要 这项工作提出了多变量 Birnbaum-Saunders 分布的对数线性模型，该模型可用于生存分析，以研究两个或多个单元的相关对数寿命。该模型是通过使用广义多元正态分布来研究的，该分布是根据正态分布的多元混合尺度构建的。所提议的多变量 Birnbaum-Saunders 线性回归模型的边际和条件线性回归模型是 Rieck 和 Nedelman 的 Birnbaum-Saunders 线性回归模型的推广 [Birnbaum-Saunders 分布的对数线性模型。技术计量学。1991;33:51-60]，已被有效地用于模拟寿命和可靠性数据。我们利用回归模型的良好分层表示来提出一种快速准确的 EM 算法来计算模型参数的最大似然估计。假设检验也是通过使用最大似然估计量的渐近正态性进行的。最后，显示了模拟研究的结果以及对真实数据集的应用，其中我们还包括此处开发的估计程序的稳健性特征。