Maximum pseudo-likelihood estimation based on estimated residuals in copula semiparametric models

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.

Automated summary

This paper discusses the estimation of the dependence structure of a multidimensional response variable in the presence of a multivariate covariate. It focuses on the parametric estimation of the copula function using the maximum pseudo-likelihood method, and proves that the estimator based on residuals has the same asymptotic distribution as the estimator based on unobserved errors under certain regularity assumptions. However, a Monte Carlo simulation study shows that the maximum pseudo-likelihood estimator based on residuals may perform poorly when the regularity assumptions are not satisfied.