The Empirical Likelihood Of A Semi-parametric Variable Coefficient Partial Linear EV Model

Semiparametric varying coefficient partially linear model is a kind of semi-parametric model with many applications in practical filed.When it was first put forward,there are lots of papers to study this model.Measurement error data is often encountered in practice.The semiparametric varying coefficient partially linear EV model gives a method to solve the problem in daily life,especially in statistical analysis for the economic,social and bi-ological data,is of great value.Statistical inference for semiparametric varying coefficient partially linear EV model has become hot research events.Hence,it has theoretical value and practical significance to investigate the statistical properties for semiparametric varying coefficient partially linear EV model.The empirical likelihood(EL),as a nonparametric statistical method,has many advan-tages over classical method.For example,the confidence region is range preserving and its shape is completely determined by the data.Variable selection is an important subject of modern statistical analysis.Using penalized empirical likelihood(PEL)method for variable selection has attracted attention of the statistician.This method can not only estimate pa-rameters and does variable selection at the same time,but also greatly reduces the amount of calculation,and overcomes the instability of the traditional variable selection method.This thesis applies the empirical likelihood to semiparametric varying coefficient par-tially linear EV model,which expands the areas of the empirical likelihood method.Firstly,we study the calibration of the EL for high-dimensional semiparametric varying coefficient partially linear EV model with measurement error data in the nonparametric parts,get the asymptotic distribution of the corrected empirical likelihood ratio.Lastly,we discuss PEL method for semiparametric varying coefficient partially linear EV model with measurement error data in the parametric parts,obtain the Oracle properties of the estimators,and give the test statistic.There are three chapters in this thesis,and the main contents are as follows.In the first chapter,we first introduce the background.Then we recall the related knowl-edge and theory of the above statistical models.At last,we list the main work.In the second chapter,aiming at the problem of the calibration of the EL for high-dimensional semiparametric varying-coefficient partially linear EV model,through the cal-culation and analysis of the statistical properties of the empirical likelihood ratio,this paper gives a new method to estimate the expectation and variance of the empirical likelihood ratio.Using this method,we get the asymptotic distribution of the corrected empirical likelihood ratio,whose asymptotic normality is better than those of the traditional method.Simulation indicates that the proposed method performs well.In the third chapter,PEL for parameter estimation and variable selection in semipara-metric varying-coefficient partially linear EV model is investigated.It is shown that the PEL estimators have the Oracle property.Also,we conclude that the asymptotic distribution of penalized empirical likelihood ratio test statistic is a chi-square distribution.The perfor-mance of the proposed method is evaluated by some simulations and real data analysis.