Semiparametric Imputation Using Conditional Gaussian Mixture Models under Item Nonresponse
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Imputation is a popular technique for handling item nonresponse in survey sampling. Parametric imputation is based on a parametric model for imputation and is less robust against the failure of the imputation model. Nonparametric imputation, such as Kernel regression imputation, is fully robust but is not applicable when the dimension of the covariates is large due to the curse of dimensionality. Semiparametric imputation is another robust imputation method that is based on a flexible model where the number of parameters in the model can increase with the sample size. In this paper, we propose another semiparametric imputation based on a more flexible model assumption than the Gaussian mixture model. In the proposed mixture model, we still assume a Gaussian model for the conditional distribution of the study variable given the auxiliary variable, but the marginal distribution of the auxiliary variable is not necessarily Gaussian. We show that the proposed mixture model based on the conditional Gaussian mixture achieves a lower approximation error bound to any unknown target density than the GMM in terms of the Kullback-Leibler divergence measure. 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 handle the real data problem in 2017 Korean Household Income and Expenditure Survey (KHIES) conducted by Statistics Korea.
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