Nonparametric Imputation For Missing Data

With the development of Internet technology, there will be an exponential growth in data volume. How to effectively mine valuable information from massive data have become an important issue in Statistics and Machine Learning. Stan-dard statistical methods have been developed to analyze complete data sets, but in practice the data are not always complete. Missing data does not mean that the information does not exist. The process of data mining and statistical inference can be badly affected by missing data.The common approaches to deal with missing data problem include deletion method, special value method and imputation method. And the imputation meth-ods, the most representative is regression imputation, performs well. Regression imputations include two forms, parametric and nonparametric. Nonparametric re-gression imputation is widely used in reality for its robust properties. The most commonly used nonparametric imputation approaches are Horvitz-Thompson in-verse weighting estimator(HT), HT ratio estimator(HTR), kernel regression impu-tation method(KR), the nearest neighbor imputation method and double-robust imputation method. On the basis of double-robust imputation method, this paper propose a new nonparametric double-robust imputation method, combining HTR and KR. A comprehensive simulation study shows that HT is most sensitive to dis-continuity in the missing data patterns, and the nearest neighbors estimators can be insensitive to missing data patterns unbalanced with respect to the distribution of the covariate, simulation study also show that new double-robust imputation method have the lowest z-score.