Coefficient Model Statistical Diagnostics And Impact Analysis

Statistical diagnostics is a new branch of statistics, which emerged and progressed rapid in recent two decades, with its intensive application background, novel statistal ideas, wide research subjects and abundant achievement. It has created a new field of stastistics, binding the theory and its application closely together.Varying-coefficient model, a strong instrument for analyzing multi-dimentionnal datas, become an importtant research field. Due to its merits of being robust, explainable and a coverage of many other models, such as additive models semiparametric regression models, linear models, it has been widely used in many fields such as biomedical,spatial measurement,ecnometic,environmental science and so on.In this paper, the statistical diagnostics and influence analysis are studied respectively for varying-coefficient models and its derivative models. At first, we give a brief description of varying-coefficient models, varying-coefficient generalized linear models, varying-coefficient EV models and statistical diagnostics. Then, we study systematically the statistical diagnostics and influence analysis for varying-coefficient linear models. The main content are as follow: under the local weighed least square estimation, we study influence analysis of the case deletion model, mean shift outlier model, the problems of testing of outlier and statistical analysis of heteroscedasticity, and obtain the diagnostic statistics, such as cook diatance, W-K statistics, likelihood distance,et al and the score test statistics, For the local influence measures ,we discuss the weighted perturbation model, mean shift perturbation model and argument perturbation model and obtain the counting formulas of influence matrics ,an simulation example are used to illustrate that our methods are available and effective. In addition, we study systematically the statistical diagnostics and influence analysis for varying-coefficient generalized linear models. The main content are as follow: Firstly, the equivalency of the case deletion model and mean shift outlier model is investigated and the simple counting formulas of some diagnostic statistics are obtained. Secondly,the local influence analysis are discussed and the counting formulas of influence marrics for case weighted perturbation model,mean shift perturbation model argument perturbation model and argument's function perturbation model are obtained. Thirdly, the testing of variance component in this model is studied and the score test statistics are obtained. At last, we study systematically the statistical diagnostics and influence analysis for varying-coefficient EV models. we study influence analysis of the case deletion model, mean shift outlier model and the problem of testing of outlier, an simulation example are provided to show that our test methods are available and effective.