Properties Of Quasi-Maximum Likelihood Estimator In Nonlinear Models

The thesis mainly studies the properties of quasi-maximum likelihood estima-tor(QMLE) in nonlinear models when response variable is q dimension , many results in literatures are extended.The thesis is divided into three parts. In the first charpter,response variable is generalized to q dimensions, we propose the concept of QMLE and quasi function in nonlinear models, then under mild conditions, we prove that there exists the solution (β|^)_n with probability 1 for sufficiently large n, and obtain the strong consistency, some results of asymptotic normality, meanwhile consistent estimator of σ~2 for QMLE for heterosedastic nonlinear models is presented.In the second charpter ,under mild conditions, we obtain the convergence rate of QMLE in nonlinear models when response variable is 1 dimension.In the third charpter, we extend the model which mentioned in reference[11] and the existence ,strong consistency and the convergence rate of QMLE are proved under certain conditions for generalized linear models with adaptive design, then we make QMLE sharper.