  Item nonresponse is frequently encountered in practice. Ignoring missing data
can lose efficiency and lead to misleading inference. Fractional imputation is
a frequentist approach of imputation for handling missing data. However, the
parametric fractional imputation of \cite{kim2011parametric} may be subject to
bias under model misspecification. In this paper, we propose a novel
semiparametric fractional imputation method using Gaussian mixture models. The
proposed method is computationally efficient and leads to robust estimation.
The proposed method is further extended to incorporate the categorical
auxiliary information. The asymptotic model consistency and $\sqrt{n}$-
consistency of the semiparametric fractional imputation estimator are also
established. Some simulation studies are presented to check the finite sample
performance of the proposed method.
