The Estimation Of Partial Linear Model And Logistic Partial Linear Model Based On Kernel Trick

In this thesis,we will introduce the high-dimensional linear regression model and Logistic regression model with multivariate nonlinear structure.Although the classical partial linear model and generalized partial linear model use the nonparametric method to solve the estimation problem of nonparametric parts to some extent,the curse of dimensionality exists when the variables of nonparametric part are high-dimensional.To avoid this problem in practice,only one-dimensional variables are used in the nonparametric part.Therefore,inspired by the use of kernel trick to deal with nonlinear regression problems,under the framework of backfitting iterative algorithm,this thesis proposes the estimation method of the partial linear model based on the kernel trick,and further tries to apply the idea of the kernel trick to the estimation of the Logistic partial linear model to solve the classification problem where the response variable is 0-1.Secondly,the effectiveness of the algorithm we proposed in this thesis is proved by numerical simulation,and the estimation results are compared with the classical partial linear models and generalized partial linear models,the accuracy and stability of the kernel trick-based estimation method is better than that of the classical estimation method.Finally,the Logistic partial linear model is applied to the credit card data to solve the binary classification problems,and the prediction effect of the model obtained by the estimation method based on the kernel trick and the classical estimation method is empirically compared.This thesis,based on the idea of kernel trick,address the shortcomings of classical partial linear model and generalized partial linear model to a certain extent.It replaces local estimation in the nonparametric part with global estimation based on the reproducing kernel.It can avoid the curse of dimensionality.Therefore,this thesis has theoretical significance and research value in the field of semiparametric model.