On Confidence Regions Of Quasi-likelihood Nonlinear Models

The quasi-likelihood nonlinear model includes the generalized linear model as a special case,which is widely used in practical problems.In this paper,the parametric confidence regions of quasi-likelihood nonlinear model with random regression,quasi-likelihood nonlinear model with random effects and quasi-likelihood nonlinear model with unknown variance are studied by using the asymptotic results of parameter estimation and the concept of curvature in these three different quasi-likelihood nonlinear models.The confidence regions of the three models are obtained.This paper is divided into five chapters.The specific work of this paper as follows:The first chapter mainly introduces the concept of generalized linear model and its parameter estimation;the background,research status and significance of quasi-likelihood nonlinear model,and the innovations of this paper.In chapter 2,the parameter confidence regions quasi-likelihood nonlinear model with stochastic regression is studied,the definition of the model is briefly introduced,and a geometric framework similar to Wei(1994,1998)is established.The confidence regions problem of parameters and subsets parameters of quasi-likelihood nonlinear models with random regressors is studied and the derivation process is given under appropriate assumptions.The corresponding results of Hamilton et al.(1982),Hamilton(1986)and Wei(1994)are extended.The third chapter mainly investigates the parameter confidence regions of quasi-likelihood nonlinear models with random effects(QLNMWRE).An improved geometric framework of Bates and Wattes is proposed.In this geometric framework,we give three improved approximate confidence regions for parameters and subset parameters.This work extends the results of Hamilton et al.In chapter 4,Based on Fang Liandi's method of studying the empirical likelihood confidence regions in nonlinear EV models with missing data,and a confidence regions with irregular results is given for the quasi-likelihood nonlinear models with unknown variance.In chapter 5,the problem of parameter confidence region of semi-parametric quasi-likelihood nonlinear model has not been reported at home and abroad,which needs to be further studied and discussed.The confidence regions of the subset parameters of the above three quasilikelihood nonlinear models lays a theoretical foundation for the study of other statistical inference problems such as hypothesis testing.The results of the existing literature are extended and developed.At the same time,the research results are more practical due to the universality of the model in practical application.