Statistic Diagnostics Of Nonlinear Models Under Box-Cox Transformation

With the rapid development of science and technology, the theory and method of statistical analysis are continuously developed and improved. 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 pneumatic, rainfall and winds 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, then probabilistic and statistical models are commonly-used in the science field, so the methods of statistical inference become the important analysis methods in systems analysis. Usually people used to use regression analysis to deal with these problems. The theory and methods of regression analysis develop rapidly. It is not only an important branch of statistics, but also widely used in all fields. With the development of regression analysis theory, nonlinear model becomes to be an important topic now. The main ideas of the paper are as follow:Chapter 2 gives the estimation parameters in the nonlinear model, meanwhile two kinds of corresponding algorithms are obtained: Gauss-Newton iterative algorithms and the improved Gauss-Newton iterative algorithms.Chapter 3 systematically discusses statistical diagnostics of nonlinear statistical model of Box-Cox transformation. The influence analysis of the model and the case-deletion model are discussed. At the same time, the equivalence of CDM and MSOM is obtained.Chapter 4 covers the methods of geometry of the nonlinear models under Box-Cox transformation, and, the structure of geometry is studied carefully. At last, we show curvature expressions of confidence region.