Jackknife Empirical Likelihood And Its Application For Semiparametric Models

The semi-parametric model produced in the 1980s combines a parametric model with a nonparametric model.It introduces nonparametric components that represent model errors or other systematic errors,so that the model contains both the parameter component and the non-parametric components.Taking into account the advantages of the parametric and the non-parametric models.It has greater adaptability than the parametric model or the non-parametric model,and has a stronger explanatory power.Least squares estimation,kernel estimation,etc.are commonly used statistical methods for studying semi-parametric models in the past.In recent years,many scholars have used empirical likelihood methods to study semi-parametric models and have obtained a large number of new results.In this paper,we use the Jackknife empirical likelihood method to study the error variance of the semi-parametric model under the martingale difference error.Also,we use the Jackknife empirical likelihood method to study the error variance of the semi-parametric model with the missing data.The Jackknife empirical likelihood ratio statistic of the error variance is proposed and it is proved that the statistic satisfies the asymptotic chi-square distribution.The first chapter introduces the research background and significance of Jackknife empirical likelihood of semi-parametric model,then introduces the research status of semi-parametric model and Jackknife empirical likelihood,and finally briefly explains the conten t structure.The second chapter introduces Jackknife empirical likelihood of error variance of partial linear varying-coefficient model under martingale error.We conclude that the error variance of the Jackknife empirical log-likelihood ratio statistic,and prove its asymptotic ?2 and obtain the corresponding empirical likelihood confidence regions.In chapter 3,the missing value is processed by interpolation method on the basis of considering the response variables missing at random,and the estimator of error variance is obtained,and the asymptotic normality of the proposed estimator is proved under the corresponding assumptions.Secondly,the Jackknife empirical log-likelihood ratio function of error variance is given,and we verified that the function satisfies the asymptotic chi-square distribution.The Jackknife empirical likelihood method can effectively reduce the bias of estimation.Studying the Jackknife empirical likelihood of the error variance of semi-parametric models will help to expand the scope of application of the semi-parametric model,and at the same time,it can be better applied to practice and provide a scientific reference for the development and progress of society.