Imputation is a popular technique for handling item nonresponse. Parametric imputation is based on a parametric model for imputation and is not robust against the failure of the imputation model. Nonparametric imputation is fully robust but is not applicable when the dimension of covariates is large due to the curse of dimensionality. Semiparametric imputation is another robust imputation based on a flexible model where the number of model parameters can increase with the sample size. In this paper, we propose a new semiparametric imputation based on a more flexible model assumption than the Gaussian mixture model. In the proposed mixture model, we assume a conditional Gaussian model for the study variable given the auxiliary variables, but the marginal distribution of the auxiliary variables is not necessarily Gaussian. The proposed mixture model is more flexible and achieves a better approximation than the Gaussian mixture models. The proposed method is applicable to high-dimensional covariate problem by including a penalty function in the conditional log-likelihood function. The proposed method is applied to the 2017 Korean Household Income and Expenditure Survey conducted by Statistics Korea.

中文翻译：

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在项目无响应下使用条件高斯混合模型进行半参数插补

插补是处理项目无响应的一种流行技术。参数插补基于用于插补的参数模型，并且对于插补模型的失败不具有鲁棒性。非参数插补是完全稳健的，但在协变量的维数很大时不适用，因为维数灾难。半参数插补是另一种基于灵活模型的稳健插补，其中模型参数的数量可以随着样本量的增加而增加。在本文中，我们基于比高斯混合模型更灵活的模型假设提出了一种新的半参数插补。在提出的混合模型中，给定辅助变量，我们假设研究变量的条件高斯模型，但辅助变量的边际分布不一定是高斯分布。所提出的混合模型比高斯混合模型更灵活，并实现了更好的近似。该方法通过在条件对数似然函数中包含惩罚函数，适用于高维协变量问题。建议的方法适用于韩国统计局进行的 2017 年韩国家庭收入和支出调查。