Moderate Deviations Of Linear EV Models With Two Kinds Of Dependent Errors

The linear EV model has been studied by many scholars since it was put forward,and it has been widely used in medicine,finance,biology and so on.The model retains the errors in the independent variables and is an extension of the simple linear model,but it is more practical than the linear model.The principle of large and medium deviations is one of the hot topics in probability theory,the core of which is the rate of convergence of rare events,compared with the central limit theorem and the classical law of large numbers,the large deviation and the medium deviation can give a more specific rate function,and can give a more accurate description of the behavior of the random variable limit of a sequence and the convergence of the parameter estimation in the model.Considering that there are two errors in the linear EV model,and the errors often depend on each other,this kind of dependence may affect the convergence of parameter estimation.Therefore,this paper studies the convergence rate of the least squares estimator in linear models with dependent random errors.The paper is divided into four chapters.The main contents are as follows:The first chapter is the introduction,this paper introduces the background and present situation of this paper,introduces the linear EV model,lists the relevant knowledge of large deviation and medium deviation theory,and expounds the main contents of this paper.The second chapter is the first important result of this paper.By using the properties of the negative correlation sequence and the Gartner-Ellis Theorem,under the assumption that the two errors in the linear model are stationary negative correlation sequences,the mid-deviation of the least square estimate of the model parameters is given and proved.The third chapter is the second important result of this paper.We mainly discuss the middle deviation of parameter estimation of linear model when two errors are stationary random sequence.According to the definition of dependent sequence,the sequence is divided into two independent parts and tail in the proof.In this paper,we use the middle deviation principle of the Independent identical distribution sequence and combine the Holder inequality to deal with it.The fourth chapter summarizes the advantages and disadvantages of the method of problem proof in this paper,and puts forward the relevant directions for further research.