  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 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 another 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. We show that the proposed mixture model achieves a lower
approximation error bound to any unknown target density than the Gaussian
mixture model in terms of the Kullback-Leibler divergence. 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 2017 Korean Household Income and Expenditure Survey conducted by
Statistics Korea. Supplementary material is available online.
