Local Modeling Algorithm Based on Similarity of Vector

A mutli-model modeling method based on local model is given. The modeling idea is firstly to find some data matching with the current working point from vast historical system input-output datasets, and in this paper, we give a new method of choose data information based on similarity of vector which improve the accuracy of data greatly. Secondly to choose the weight and optimum bandwidth then develop a local model using local polynomial fitting algorithm. With the change of working points, multiple local models are built. The effectiveness of the proposed method is demonstrated by simulation results.

Two-Stage Method Based on Local Polynomial Fitting for a Linear Heteroscedastic Regression Model and Its Application in Economics

We introduce the extension of local polynomial fitting to the linear heteroscedastic regression model. Firstly, the local polynomial fitting is applied to estimate heteroscedastic function, then the coefficients of regression model are obtained by using generalized least squares method. One noteworthy feature of our approach is that we avoid the testing for heteroscedasticity by improving the traditional two-stage method. Due to nonparametric technique of local polynomial estimation, we do not need to know the heteroscedastic function. Therefore, we can improve the estimation precision, when the heteroscedastic function is unknown. Furthermore, we focus on comparison of parameters and reach an optimal fitting. Besides, we verify the asymptotic normality of parameters based on numerical simulations. Finally, this approach is applied to a case of economics, and it indicates that our method is surely effective in finite-sample situations.

UNIFORM BAHADUR REPRESENTATION FOR LOCAL POLYNOMIAL ESTIMATES OF M-REGRESSION AND ITS APPLICATION TO THE ADDITIVE MODEL

We use local polynomial fitting to estimate the nonparametric M-regression function for strongly mixing stationary processes {(Yi,Xi)}. We establish a strong uniform consistency rate for the Bahadur representation of estimators of the regression function and its derivatives. These results are fundamental for statistical inference and for applications that involve plugging such estimators into other functionals where some control over higher order terms is required. We apply our results to the estimation of an additive M-regression model.