Nonparametric Imputation Under Random Missing Model

Whether it was in the slow years of computer development in the last centu-ry,or in the age of big data,human beings are confronted with huge data mining and imputation of missing values.The interpolation problem of missing data has been studied by scholars since the 1950s.In general,the methods of incomplete data have special value substitution method,the method of parameter estimation,bayesian estimation method and so on.This paper mainly studies data imputation method.The mean imputation method is simple and easy,which is widely used in various fields.However,it ignores the data correlation and distance relationship between observe values and missing values,thus it has its own disadvantages.An-other method is the nearest neighbor estimation method,which uses the observed value and its associated intensity near the missing value relations to interpolate the loss value.The traditional imputation methods also have the inverse probability weighting method,the kernel density regression method and so on.Academics have put forward combining the inverse probability weighting im-putation method with the kernel regression imputation method to construct the new estimator.In this paper,considering the robustness of the inverse probabil-ity weighting imputation method is superior to the kernel regression imputation method,two kinds of convex mixed imputation estimators are constructed based on the advantages of inverse probability weighted imputation and nearest neighbor imputation method and the asymptotic properties of the two are proved under the regular conditions.Whether the regression function is continuous or not,the sim-ulation results show that the simulation effect of two mixed imputation estimators is better than that of traditional imputation method.In irises data analysis,the comparison of three kinds of imputation estimator is better than others.Convex mixed estimator in the data analysis of the average absolute deviation obviously superior to other two imputation methods in wine quality data.