Tarying-coefficient Partially Linear Model Of Parameter Estimation And Statistical Diagnosis

Varying-coefficient partially linear model is a hot topic of current research, which does not only inherit the stability of the non-parametric regression and other characteristics, while retains the other advantages such as the intuition of the linear model and easily explained, so the varying-coefficient linear model is widely favoured by the domestic and foreign scholars, and is also applied to the economics and finance, especially for high dimensional data, theses models are widely used.In this paper, based on the existing varying coefficient linear regression models, it discusses the parameter estimation of the varying coefficient partially linear models, which are derivative from the varying coefficient linear regression models, statistic diagnosis and the outlier testing ect. from different aspects. Firstly, the paper briefly summarizes the history and current situation of the parameter estimation and the statistical diagnosis, and introduces the two important concepts in the statistic diagnosis, which are outliers and influential point, and also demonstrates the Score Statistic, then briefly describes the main content of this paper. Secondly, it gives a brief description of the variable coefficient linear models, and the statistics diagnosis, based on the locally weighted least squares, the influential analysis of the statistic deletion models, and the results of the mean drift models and the outlier test etc. are given; Further more, the parameter estimation and the statistic diagnosis of the vary coefficient partially linear models are mainly studied in this paper. In this section, it discusses the common method of estimation of the varying coefficient partially linear models, then based on the two-stage quasi-maximum likelihood method, the estimations of the unknown parameters and the coefficient function are given, and it discusses the asymptotic properties of estimators in statistical diagnosis. And in the statistic diagnosis, the influence analysis of the vary coefficient partially linear models'deletion case and the mean drift models formula are studied. And the equivalence of the mean drift model and vary coefficient partially models is discussed, and then the outlier testing method is drawn, the diagnosis statistics, such as the Cook Distance, W-K statistic, and the Likelihood Distance etc, and the Score test statistic. Finally, through the example of the on-site simulation results, it dicates that these testing methods are effective and feasible.