This paper investigates the estimation of parametric copula models when the data have nonignorable nonresponse. We consider the propensity follows a general semiparametric model, but the distribution of the response variable and related covariates is unspecified. To solve the identifiability problem, we use an instrumental covariate, which is related to the response variable but unrelated to the propensity given the response variable and other covariates. The generalised method of moments is applied to estimate the parameters in the propensity. Based on kernel-assisted regression approach, we construct the bias-corrected semiparametric estimating equations to improve estimation efficiency. Consistency and asymptotic normality of the proposed estimators are established. The finite-sample performance of the estimators is studied through simulation, and an application to HIV-CD4 data set is also presented.

中文翻译：

---

具有不可忽略缺失数据的 copula 模型的半参数估计

本文研究了当数据具有不可忽略的非响应时参数 copula 模型的估计。我们认为倾向遵循一般的半参数模型，但未指定响应变量和相关协变量的分布。为了解决可识别性问题，我们使用工具协变量，它与响应变量相关，但与给定响应变量和其他协变量的倾向无关。应用广义矩法来估计倾向中的参数。基于核辅助回归方法，我们构造了偏差修正的半参数估计方程，以提高估计效率。建立了建议估计量的一致性和渐近正态性。通过模拟研究估计器的有限样本性能，