Linear Representation And Robust Test Of The M-estimation In GLM

Generalized linear models(GLMs),which have been introduced by Nelder and Wedderbum(1972),are widely used in data analysis.In this paper we consider the model yi=h(xiT?)+ei,i=1,2,...,n,where the dependent errors defined as ei=G(...,?i-1,?i),h is a continuous differentiable function,?i are independent and identically distributed(i.i.d.)random errors with zero mean and finite variance ?2,G is a measurable function.In chapter 2,we consider the M-estimator for generalized linear models with dependent error.We also show the weak and strong Bahadur representation and asymptotic normality of the estimator,which extend the correspondingly results of linear regression models to the generalized linear model.In chapter 3,we study the strong Bahadur representation of the M-estimator.In chapter 4,we consider robust test for generalized lineal models with dependent errors.Under the error hypothesis and general linear hypothesis,we derive the asymptotic distribution of the test,which extend the Heritier and Ronchetti(1994)results to the generalized linear models with dependent errors.Above studies allow us to present more simple asymptotic distribution for the robust test under specific conditions.In chapter 5,Firstly,the application of Bahadur representation illustrate the breadth and validity of conclusions;Secondly robust test conclusions are given practical examples that illustrate the application of the conclusions of the feasibility and correctness.