Neural Network Based Non-Parametric Regression With Missing Data And Its Application

Neural Network has achieved great success in image recognition,pattern recognition,artificial intelligence as a machine learning algorithm.Neural network has acquired great attention especially in the area of statistics,and has been applied to problems like non-parametric regression.However,in practical use of statistics,the completeness of data in practical usage of statistics can't be always assured.It is difficult to deal with missing data.Using neural network on non-parametric regression problems should also consider the solutions to missing data.So we modify the existing methods under the premise of missing data.According to different types of missing data,there might be missing response variables or covariate variables.In order to deal with missing data under missing at random assumption,we propose inverse probability weighted and kernel imputation based non-parametric regression approaches.Inverse probability weighted method can be applied in both two conditions,while kernel imputation based non-parametric regression approaches can only be suitable for the condition of missing covariates.We prove the Unbiasedness of the estimators under these condition as well.The effectiveness of the proposed method is verified through simulation studies.Finally,we apply the proposed approach to deal with real data.