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Nonparametric regression imputation is commonly used in missing dataanalysis.  However, it suffers from the ``curse of dimension".  The problem can be alleviated by the explosive sample size in the era of bigdata, while the large-scale data size presents some challenges on the storageof data and the calculation of estimators.  These challenges make the classical nonparametric regression imputationmethods no longer applicable.  This motivates us to develop two distributed nonparametric regressionimputation methods.  One is based on kernel smoothing and the other on the sieve method.  The kernel-based distributed imputation method has extremely lowcommunication cost and the sieve-based distributed imputation method canaccommodate more local machines. To illustrate the proposed imputation methods,response mean  estimation is considered.  Two distributed nonparametric regression imputation estimators are proposedfor the response mean, which are proved to be asymptotically normal withasymptotic variances achieving the semiparametric efficiency bound.  The proposed methods are evaluated through simulation studies and areillustrated by a real data analysis.

Distributed nonparametric regression imputation for missing response problems with large-scale data