Empirical Likelihood For Generalized Linear Models With ARCH Errors

Generalized linear models are the generalization and development of classical linear regression models,it has a very important application in many fields such as economy,medicine,biology,social statistics,management and so on.At present,we consider the generalized linear models of the error terms are generally subject to normal distribution,t distribution,etc.,this requirement is very harsh in practical applications,especially in the some of economic problems,the error does not obey the normal distribution,but obey the heavy tail distribution.The ARCH model has the characteristic of describing the clustering of the fluctuation,and it also determines that its unconditional distribution is a spike and thick distribution.Therefore,this paper combines the ARCH model with the generalized linear models to consider the error terms of the generalized linear models obey the ARCH model to study some of the excellent properties of the two models.The empirical likelihood method has many excellent properties and has been widely applied to various statistical models and fields.In this paper,the smoothed empirical likelihood method is introduced into the generalized linear models with ARCH errors,and we structure the smoothed empirical log-likelihood ratio statistics to study the model parameters confidence interval of the relevant issues.The structure is as follows:The first chapter,we mainly introduces the background of the model and the research status at home and abroad in the exordium.The second chapter,the paper expounds the generalized linear models?ARCH model and empirical likelihood of related content.The third chapter,we discuss the generalized linear models with ARCH errors,apply the LAD estimation method and the smoothed empirical likelihood method to construct the estimation of the unknown parameters in the model,and verify the asymptotic of the LAD estimator and the smoothed empirical likelihood estimator,gives the confidence interval of the corresponding parameters.The fourth chapter,numerical simulations are conducted to compare the coverage of the confidence interval obtained by the smoothed empirical likelihood method with the coverage of the confidence interval obtained by the asymptotically normal method.The simulation results show that the smoothed empirical likelihood method has a better coverage and confidence interval than the asymptotic normality method,in small sample case,the effect is more significant.In the fifth chapter,we prove the relevant theorem in this paper.In the sixth chapter,summary and outlook.