Variance Homogeneity Examination Of Nonlinear Random Effect Models With Right Censored Data

With the rapid development of science and technology, the theory and method of statistical analysis are continuously developed. In the process of statistical analysis, it is a very important research topic to establish a mathematical model. For example,the engineers of steelworks want to have a mathematical model about the process of steelmaking to implement computer automatic control; weather researchers want to have a mathematical model about depression, rainfall and wind speed to forecast weather;the experts on urban planning want to have a mathematical model about a large system including population, traffic, energy and pollution to provide the scientific basis to help leadership to make urban development planning and decision-making. Many complex systems usually contain uncertainty, so probabilistic and statistical models are commonly used, hence the methods of statistical inference become the important methods in systems analysis. Usually people used to use regression analysis to deal with these problems. It not only become an important branch of statistics, but also widely used in other fields. With the development of regression theory, the random effects model has become an important research topic.Random effects model includes linear and nonlinear model, the variance of random effects model includes within-dividual and inter-individual variability. In recent years, there is a large number of literatures on the parameters estimate, statistics diagnosis, impact analysis in linear mixed effects models, in these studies, the homogeneity of variance assumption is often used. Seber and Wild(1989) studied several examples, pointing out that the homogeneity of variance assumption is often inappropriate in the regression analysis. Therefore,we must test their homogeneity of variance. There are many results on the homogeneity test of variance in the linear and nonlinear regression model. Zhang and Weiss discussed the heteroscedasticity hypothesis testing of the linear mixed model. The nonlinear mixed effects model is more difficult, and there are not too many research results. This paper mainly discusses the test of homogeneity of variance problems in the nonlinear random effects model with right-censored data, which is developed from the nonlinear random effects model.Chapter I mainly introduces the nonlinear random effects model with right-censored data , and summarizes our research work.The second chapter discusses parameters estimate in the nonlinear random effects model with the right-censored data, and the Gauss-Newton iterative algorithm is given , meanwhile the improved Gauss-Newton iterative algorithm is developed.Chapterâ…¢covers heteroscedasticity test in the the random effects model with right-censored data. Several frameworks of heteroscedasticity test, such as within-dividual and inter-individual homogeneity. Score statistics are given. At last, a numerical example is given to illustrate the avaiablity of our results.