Semiparametric Imputation Using Conditional Gaussian Mixture Models\n under Item Nonresponse

Imputation is a popular technique for handling item nonresponse in survey\nsampling. Parametric imputation is based on a parametric model for imputation\nand is less robust against the failure of the imputation model. Nonparametric\nimputation is fully robust but is not applicable when the dimension of\ncovariates is large due to the curse of dimensionality. Semiparametric\nimputation is another robust imputation based on a flexible model where the\nnumber of model parameters can increase with the sample size. In this paper, we\npropose another semiparametric imputation based on a more flexible model\nassumption than the Gaussian mixture model. In the proposed mixture model, we\nassume a conditional Gaussian model for the study variable given the auxiliary\nvariables, but the marginal distribution of the auxiliary variables is not\nnecessarily Gaussian. We show that the proposed mixture model achieves a lower\napproximation error bound to any unknown target density than the Gaussian\nmixture model in terms of the Kullback-Leibler divergence. The proposed method\nis applicable to high dimensional covariate problem by including a penalty\nfunction in the conditional log-likelihood function. The proposed method is\napplied to 2017 Korean Household Income and Expenditure Survey conducted by\nStatistics Korea. Supplementary material is available online.\n