This paper deals with an estimation of the dependence structure of a multidimensional response variable in the presence of a multivariate covariate. It is assumed that the covariate affects only the marginal distributions through regression models while the dependence structure, which is described by a copula, is unaffected. A parametric estimation of the copula function is considered with focus on the maximum pseudo-likelihood method. It is proved that under some appropriate regularity assumptions the estimator calculated from the residuals has the same asymptotic distribution as the estimator based on the unobserved errors. In such case one can ignore the fact that the response is first adjusted for the effect of the covariate. The theoretical results are accompanied by a Monte Carlo simulation study which illustrates that the maximum pseudo-likelihood estimator based on residuals may behave poorly when the stated regularity assumptions are not satisfied.

中文翻译：

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基于 copula 半参数模型中估计残差的最大伪似然估计

本文涉及在存在多元协变量的情况下对多维响应变量的依赖结构的估计。假设协变量仅通过回归模型影响边缘分布，而由 copula 描述的依赖结构不受影响。copula函数的参数估计被认为是最大伪似然法。证明了在一些适当的规律性假设下，从残差计算的估计量与基于未观察到的误差的估计量具有相同的渐近分布。在这种情况下，人们可以忽略响应首先针对协变量的影响进行调整的事实。