A Further Study Of Theory In Quasi-likelihood Nonlinear Models

The thesis mainly studies the properties of quasi-maximum likelihood estimator(QMLE) in nonlinear models , many results in literatures are exended. The thesis summarize various methods preiously, base on the strong consistency and convergence rate of maximum quasi-likelihood estimates of quasi-likelihood estimate model with a fixed design, then studies the large sample properties of maximum quasi-likelihood estimates of QMLE in nonlinear models which variance is unknown.. The thesis mainly studies the strong consistency and convergence rate of maximum quasi-likelihood estimates which variance is unknown.The thesis is divided into four parts. In the first chapter, we introduce the history of generalize linear mode at first, then we introduce the quasi-likelihood estimate model and the results of previous studies, etc.In the second part, we introduce the generalize linear mode at first, then we introduce the link function and the natural link function, maximum likelihood estimate and maximum quasi-likelihood equation. Then we get the definition of maximum quasi-likelihood estimate and quasi-likelihood equation.In the third part, we discuss the strong consistency of maximum quasi-likelihood estimation in quasi-likelihood nonlinear models when the variance function is unknown. When meet the assumptions, then there isβ0of which maximum quasi-likelihood estimation proposed sequence is {β? n}, With probability 1, when n is sufficiently large, the maximum quasi-likelihood equation U n (β? n) = 0has a solution, andβ? n→β0a. s . ( n→∞)In the forth part, we discuss the speed of strong consistency of maximum quasi-likelihood estimation in quasi-likelihood nonlinear models when the variance function is unknown. When meet the assumptions, then there isβ0of which maximum quasi-likelihood estimation proposed sequence is {β? n}, make:...