Abstract To estimate distribution functions and quantiles of a response variable when the data having nonignorable nonresponse and the dimension of covariate is not low, this article assumes that the propensity follows a general semiparametric model, but the distribution of the response variable and related covariates is unspecified. To address the identifiability problem, an instrumental covariate, which is related to the response variable but unrelated to the propensity given the response variable and other covariates, is used to construct sufficient instrumental estimating equations. Three different semiparametric estimation methods are developed based on inverse probability weighting, mean imputation, and augmented inverse probability weighting. Furthermore to improve the efficiency and alleviate the curse of dimensionality, the sufficient dimension reduction technique is employed to produce efficient kernel estimation, and a class of dimension-reduced estimators for distribution functions and quantiles is proposed. Consistency and asymptotic normality of the proposed estimators are established. It can be shown that these estimators are asymptotically equivalent. 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：

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具有不可忽略非响应的分布函数和分位数的降维半参数估计

摘要 为了在数据具有不可忽略的非响应且协变量维数不低时估计响应变量的分布函数和分位数，本文假设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，使用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的工具协变量来构建足够的工具估计方程。基于逆概率加权、均值插补和增广逆概率加权开发了三种不同的半参数估计方法。此外，为了提高效率和缓解维数灾难，充分降维技术被用来产生有效的核估计，并提出了一类用于分布函数和分位数的降维估计器。建立了建议估计量的一致性和渐近正态性。可以证明这些估计量是渐近等价的。通过模拟研究了估计器的有限样本性能，还介绍了对 HIV-CD4 数据集的应用。