Consistency And Asymptotic Of The Maximum Quasi-likelihood Estimator In Generalized Linear Models

Generalized linear models as the extended of classical linear model, making it suit-able for discrete data, especially disaggregated data. Generalized linear models includinga large number of excellent properties, in actual applications, this properties allows re-searchers to obtain satisfactory results. therefor scholars attach importance to generalizedlinear models once it brought up, as more and more related research achievement ap-plied to statistical software, generalized linear models become a very important tool forresearch education, economic,sociology、medical、biology、geological survey and otherissues in the field.This paper main research some large sample properties of the maximum quasi-likelihood estimator in generalized linear models, Such as：asymptotic existence, asymp-totic normality and consistency. Through summary of the various methods of conven-tional, promotion the relevant conclusions of the maximum quasi likelihood estimator ingeneralized linear model.Firstly, we discuss the one-dimensional generalized linear models with weak consis-tency of maximum quasi likelihood estimation. Under the regular condition of relativelyweaker than literature [12](Zhang Sanguo,2007), spread the relevant conclusions of natu-ral link to unnatural link, proved that a necessary condition for weak consistency and con-vergence speed of maximum quasi-likelihood estimation, such that βn β0=op(λ1/2n).Secondly, this paper reference the processing idea of literature [22](Tang Nian-sheng,2010) for large sample properties of nonlinear reproductive dispersion models, proved that under the condition of nature link, asymptotic properties of the maxi-mum likelihood estimator in multidimensional generalized linear models.Finally, aiming at the question raised by literature [23](Xia Tian,2008), under theappropriate assumptions and other smooth conditions, use more simple method provedthat asymptotic existence of the solution of quasi-likelihood function in quasi-likelihoodnonlinear models, and obtained the rate of the solution converges to the true value is∥β n β0∥=O(n (δ1/2)(log log n)1/2).