Semiparametric Conditional Quantile Estimation Through Copula-Based Multivariate Models
提出一种基于Copula函数的分位数回归新方法，通过Copula和边缘分布估计得到响应变量的加权分位数，适用于独立同分布和时间序列数据，且能直接处理多个协变量。
We consider a new approach in quantile regression modeling based on the copula function that defines the dependence structure between the variables of interest. The key idea of this approach is to rewrite the characterization of a regression quantile in terms of a copula and marginal distributions. After the copula and the marginal distributions are estimated, the new estimator is obtained as the weighted quantile of the response variable in the model. The proposed conditional estimator has three main advantages: it applies to both iid and time series data, it is automatically monotonic across quantiles, and, unlike other copula-based methods, it can be directly applied to the multiple covariates case without introducing any extra complications. We show the asymptotic properties of our estimator when the copula is estimated by maximizing the pseudo-log-likelihood and the margins are estimated nonparametrically including the case where the copula family is misspecified. We also present the finite sample performance of the estimator and illustrate the usefulness of our proposal by an application to the historical volatilities of Google and Yahoo.