Error Of The Ar (1) Semi-parametric Regression Models And Statistical Analysis

In recent years, the research of semi-parametric regression model has attracted considerable attention and becomes an important field in the regression analysis. Semi-parametric regression model can be seen as mixed model of the parametric linear model and the nonparametric regression model, it is extensions of linear model. It has relaxed the assumption of certain explanatory variable in linear model, causes the model adaptation data change ability to be stronger. Semi-parametric regression model, useful in many problems especially for econometrics, medical, experimental design, GPS localization, is an excellent generalization from linear regression model.This paper discusses the semi-parametric regression model with first-order auto-regressive errors, especially for the method and application of the diagnostics. The penalized least square estimation of the model is given first. The D-W test and Score test are proposed to test the autocorrelation and heteroscedasticity of the random errors in semi-parametric model. Then, we get the concise expressions based on case deletion model, establish an equivalence between the case deletion model and mean shift outlier model from which we derive tests for outliers. The basic diagnostic statistics such as residuals, generalized leverage, Cook distance, penalized likelihood displacement et al. are introduced. Finally, we also discuss the local influence analysis and get concise influence matrix for case weight perturbation and perturbation of response. Numerical examples are given to illustrate our diagnostics methods.