Improvements And Applications Of Nonparametric Regression Interpolation Method With Missing Response Variables

The problem of missing data generally exists in all fields.If the incomplete data set is used directly,it may have an adverse effect on the quality of subsequent statistical analysis.Therefore,the treatment of missing data has gradually become the research focus of statisticians.Common missing data processing methods include deletion method,regression interpolation method and multiple interpolation method.The deletion method may lose some important information,and the operation process of multiple interpolation method is complicated.By contrast,the regression interpolation method has a wider application range.Regression interpolation method is divided into parametric regression interpolation method and nonparametric regression interpolation method.Because nonparametric regression interpolation method does not make specific assumptions about regression form,its interpolation is relatively robust.In this paper,an improved nonparametric regression interpolation method is proposed to deal with the random missing of response variables.Traditional nonparametric regression interpolation methods include kernel density interpolation,nearest neighbor interpolation and inverse probability weighted interpolation.In recent years,some scholars have combined the nearest neighbor interpolation method with the kernel density interpolation method,and proposed a convex hybrid interpolation method with double robustness.Considering the different sensitivity of kernel density regression function and nearest neighbor regression function to the continuity of trend function,the position of trend function in convex mixed regression function was adjusted to form a new mixed regression function.According to the new mixed regression function,firstly,the (?)_CM1 and?(?)_CR1 interpolation estimators are constructed for the overall mean value with missing response variables,secondly,the(?)_MCMinterpolation estimators are constructed by replacing the sample size with valid samples,and then the asymptotic normality of these three new mixed interpolation estimators is proved under regular conditions,and the(?)_CM1,?(?)_CR1 and?(?)_MCMinterpolation estimators are compared with kernel density,nearest neighbor and convex mixed interpolation estimators.In this paper,the superiority of the improved nonparametric regression interpolation method is verified by simulation research,and its application value is illustrated by empirical application.In the simulation study,the interpolation estimators are evaluated according to five evaluation indexes,namely mean absolute deviation,mean square error,CCI,ZS and Q.The simulation results show that the comprehensive interpolation effect of?(?)_CM1 and?(?)_MCMinterpolation estimators is the best.The trend is discontinuous,the mean absolute deviation of the three new interpolation estimators is less than the kernel density interpolation estimator,and the mean square error is less than the nearest neighbor interpolation estimator.When predicting the residual resistance per unit displacement of sailboat,the improved interpolation method is better than the kernel density and nearest neighbor interpolation method in terms of the average absolute error of missing value prediction.From the accuracy of missing value prediction,the improved interpolation method is the best.When estimating the overall mean of PM2.5 in Beijing,when the missing rate is 13%,the absolute deviation of?(?)_CR1 and?(?)_CM1 interpolation estimators is less than that of kernel density,inverse probability weighting and convex mixed interpolation estimators.When the missing rate is 42%,the absolute deviation of?(?)_MCMinterpolation estimator is the smallest.The application shows that the improved nonparametric interpolation method proposed in this paper is practical and can be applied to students.