Linear Statistical Model Perturbation Analysis And Local Nonlinear Estimation

The namely linear statistical model refers to one of the most widely used models in modern statistics, which lays a basic foundation for other statistical models. One of the important elements is parameter estimation in the linear statistical model. As we all known, the measureble and calculative errors are still under consideration in the practical experience, and the data that we had got during the experience is only approximate to the practical true value, with which some errors and perturbation to some extent. One of the research contents is the effect of independent variable data perturbation for parameter estimation. In the practical experience, model varible is spatical correlation, through assumption regression coefficients are other varibles unknown functions to increase flexibility and adaptability, with the help of the promotion of linear models the spatially varying-coefficient model is available. The geographical weighted regression method had played an effective role in dealing with problems emerged in the so-called spatially varying-coefficient such as the non-stationary and the estimation of model parameters. This paper presents an improved estimation method in thespatially varying-coefficient model.This thesis consists of two parts:Firstly, this study bases on the basic form of the linear model, the research tool is featuring by the least square estimation, eigenvalue perturbation and Hermite matrix. Then we conduct to research that focus on the problem of data perturbation, and try to summarize the sufficient condition of the model parameter which can be estimated when data is perturbed, and further discuss the effect of data perturbation on the model parameter, and finally conclude the estimation expression of the model parameter.Secondly, the spatially varying-coefficient model has been widely used in many fields. This paper bases on the local linear GWR, and tries to summarize the non-linear fitting method of this spatially varying-coefficient model. Through the case study on the local nonlinear GWR method, and finally conclude that the unique GWR method has better estimation effect on the estimation of coefficient function.