Quasi-maximum Likelihood Estimation And Its Application In Generalized Linear Models With FCA Errors

Generalized linear model is widely used in medical science, biology science,insurance, economy, social and so on. As the natural extension of classical linearmodel, it can be used in continuous data and discrete data.Functional coefficientautoregressive is also widely used in many aspects such as Wolf black words,American GNP, Dutch guilder, dollar exchange rate and so on. Therefore, generalizedlinear models under FCA errors are obtained by combining the generalized linearmodel with function coefficient autoregressive process, which has great theoreticalsignificance and extensive applicational value.In chapter II,using the method of quasi maximum likelihood estimation,wediscuss generalized linear models with FCA errors. We get the quasi maximumlikelihood estimators of unknown parameters, and prove the existence and uniquenessand the weak consistency of quasi maximum likelihood estimators.In chapter III,we firstly study the asymptotic normality of quasi maximumlikelihood estimators.We discuss the problems on hypothesis test by the method ofquasi likelihood ratio,and obtain the asymptotically chi-square distribution of quasilikelihood ratio statistics.In chapter IV,for the data from an enterprise employee individual income inHeiLongjiang Province,we build generalized linear models with FCA errors and thenwe analysis this model.It is shown that our model is superior to generalized linearmodel.