Local Influence In Semi-parametric Nonlinear Reproductive Dispersion Models

Data and model extracted from the actual problems are only an approximative description of complex process, which inevitably contains some assumptions. In order to overcome the inconsistencies that existed between the established model and the objective reality, people begin to study the statistical diagnostics, which is an important step on dealing with the data and have improtant significance in theory and practice. In the middle of 1980s, Engel et al (1986) while studying the relation between weather and electricity sales,proposed an important statistical model, that is semiparametric regression model. There are the parametric part and nonparametric part in the model. A number of practical problems can be described through this model.The information of data can be used fully and it is more ture than parametric models and nonparametric models. The semiparametric nonlinear reproductive dispersion models are the natural extension of the semiparametric models, index nonlinear models, generalized linear model and normal nonlinear regression model. In this paper, the statistical diagnostics are studied for these models. At last, we establish semi-parametric model of the Gini coefficient of Chinese residents to illustrate the feasibility, effectiveness and application value of local influence analysis method. The main results of this paper are as follows:1. In the first chapter, we give a brief description of the semiparametric nonlinear reproductive dispersion models (SNRDM); Secondly, we also introduce the background and present conditions for statistical diagnostics; Finally, the main work of this paper are introduced.2. In the second chapter, we study systematically the parameter estimation for semiparametric nonlinear reproductive dispersion models. Firstly we given the definition of semiparametric nonlinear reproductive dispersion models ,Then we derive density function for this model; At the last, we solve the model parameters through iteration method.3. In the third chapter, we study statistical diagnoses of semiparametric nonlinear reproductive dispersion models by local impact analysis.The main results are sa follows: we first give a brief description of the local influence analysis, and define the diagnostic statistics such as Cook distance,et; then we discuss respectively the local impact analysis for the weighted disturbance model and the response variable disturbance model , and the impact matrix formula are derived; last, a real example (Gini coefficient of Chinese residents) is provided to illustrate that our method is availanle.In summary, the statistical diagnostics and influence analysis are studied systematically for semiparametric nonlinear reproductive dispersion models, The results of Cook (1977,1986), Wei bo cheng, etc. (1991), Zhong & Wei (1999), Zhang hao(2007), Tang niansheng (2001) are extended and improved. Examples and some simulations are provided to illustrate that our methods are simple and available. These results are not only useful in theory, but also significant in practice.