标题： 多元线性回归模型中条件分位数的联合估计 — 金融困境的应用 显示英文标题

标题： Joint estimation of conditional quantiles in multivariate linear regression models. An application to financial distress

摘要： 本文提出了一种最大似然方法，在线性回归框架下联合估计多元响应变量的边缘条件分位数。 我们考虑了 Kotz 等人（2001）提出的多元非对称拉普拉斯分布的轻微重新参数化，并利用其位置-尺度混合表示来实现一个新的EM算法以估计模型参数。 这个想法是将非对称拉普拉斯分布与著名的单变量分位数回归模型之间的联系扩展到多元环境中，即当涉及多元因变量时。 该方法考虑了多个响应变量之间的关联，并研究响应变量与解释变量之间关系如何在响应变量的边缘条件分布的不同分位数上变化。 还提出了惩罚版的EM算法来解决变量选择问题。 我们的方法的有效性在模拟研究中进行了分析，我们还提供了证据表明所提出的方法比通过单独的单变量分位数回归获得的估计效率更高。 最后，提出一个实际数据应用来研究意大利公司样本中财务困境的主要决定因素。 显示英文摘要

摘要： This paper proposes a maximum-likelihood approach to jointly estimate marginal conditional quantiles of multivariate response variables in a linear regression framework. We consider a slight reparameterization of the Multivariate Asymmetric Laplace distribution proposed by Kotz et al (2001) and exploit its location-scale mixture representation to implement a new EM algorithm for estimating model parameters. The idea is to extend the link between the Asymmetric Laplace distribution and the well-known univariate quantile regression model to a multivariate context, i.e. when a multivariate dependent variable is concerned. The approach accounts for association among multiple responses and study how the relationship between responses and explanatory variables can vary across different quantiles of the marginal conditional distribution of the responses. A penalized version of the EM algorithm is also presented to tackle the problem of variable selection. The validity of our approach is analyzed in a simulation study, where we also provide evidence on the efficiency gain of the proposed method compared to estimation obtained by separate univariate quantile regressions. A real data application is finally proposed to study the main determinants of financial distress in a sample of Italian firms.