Bagging Method For Nonparametric Regression Analysis

At present,nonparametric regression has attracted widespread attention in many fields.N-W kernel estimation is an important method in nonparametric regression.The theoret-ical and experimental results show that the N-W kernel estimation is greatly affected by smoothing bandwidth,and its prediction results are not good enough in many cases,espe-cially in the marginal region of the input value.At the same time,according to the domestic literature,it is difficult to find a new creative method in nonparametric regression anal-ysis.It has certain research significance to use the new method to solve the problem of excessive prediction error when using the traditional N-W kernel estimation method in nonparametric regression.In order to improve the prediction accuracy of N- W kernel estimation,the follow-ing two research work has been done in this paper.1.Combining the idea of Reproducing Kernel Hilbert Space with the traditional N-W kernel estimation method on the basis of Bagging theory,the Bagging method of RKHS kernel estimation is proposed,which is simply called RKHS method.2.In order to further reduce the prediction error,the Bagging method of RKLL kernel estimation which is simply called RKLL method is proposed with the theory of Bagging by combining the idea of local linear,the Reproducing Kernel Hilbert Space and the N-W kernel estimation.The results of simulation experiments show that for general samples,the prediction error of RKLL method is much smaller than that of the other two methods,and sometimes even more than one hundred times smaller than N-W kernel estimation.The prediction error of RKHS method is usually between RKLL and N-W kernel estimation.At the same time,RKLL method and RKHS method have solved the boundary effect problem of N-W kernel estimation method.The selection of smoothing bandwidth and reproducing kernel are still important factors affecting the prediction results of RKLL method and RKHS method.