Researching Of The Non-Parametric Regression Estimation Model Of The Local Polynomial

This paper mainly studies the nonparametric regression estimation model of local polynomial. It is a very important regression estimation model of non-parameter statistics. It's better than the kernel estimaion method to reflect the relationship between variables. In the economic, financial and social sciences, the model has important application value. Therefore, it's very important to research the nonparametric regression estimation model of local polynomial by cautiously. This paper mainly studies the following several aspects.Firstly, we introduce the research situation of the local polynomial regression estimation and its basic concept from the model's background. Then, we discuss the linear regression model, the nonparametric regression model, the least-square estimation method, kernel function and kernel estimation method. We give the concept of the linear smoother. We prove the propositions and conclusion which we have.Secondly, we study the estimator r (x) of the nonparametric regression estimation model of local polynomial and give the mean and variance of the (r|^)_n (x). We give the concept of the leave-one-out cross-validation score. We also discuss the best method to choose the bandwidth and give the best value of it. We use the nonparametric regression estimation model of local polynomial and polynimial estimation model to analyze the relation between the urban consumption and the foreign exchange reserves, and obtain the two models'fitting and the fitted curve. We know that the nonparametric regression estimation model of local polynomial is superior to polynomial estimation model in the economic analysis by comparing the fitting with the practical value, comparing with the two fitted curves and comparing with models'MSE.Thirdly, we introduce the difference sequence from the methods of Neumann, et al, and get the variance estimation in the nonparametric regression estimation model of local polynomial via difference sequence method based on Hall, Kay and Titterington's method. We give the best bandwidth and the global mean squared risk of the variance estimation (V|^)_h (x). We discuss that the variance estimation (V|^)_h (x) is asymptotically normal.