Penalized Empirical Likelihood Of Partial Linear Models And Generalized Linear Models

Partly linear model was first proposed by Engle in 1986,followed by a large number of studies and applications.Generalized linear model,which was proposed by Nelder and Wedderburn in 1972,is an important generalization of the linear model.This model is widely used in the fields of society,economy,biology and medicine.In many practical problems,we may encounter the situation that the covariates are measured with errors.In addition,with the development of science and technology,data often appear in the form of high dimensional.Therefore,the statistical study of the partial linear model with measurement error in all variables and high dimensional generalized linear model have practical value.Empirical likelihood is a nonparametric statistical method proposed by Owen in 1988.It has a lot of outstanding advantages,for example,objective determination of the shape of the confidence region,Bartlett correctability,etc.As a new method,empirical likelihood has been applied to various statistical models and different fields.In recen-t years,data are usually in the form of high dimensional.Therefore,using effectively variable selection to excavate effective information from high dimensional data becomes the focus of attention.In view of the characteristics of traditional variable selection,s-tatisticians proposed penalty function,which can select variables and estimate parameters simultaneously.This method has been widely used over this years.In this paper,we apply penalized empirical likelihood to the partially linear model with measurement error in all variables and high dimensional generalized linear model.This applications extend the application field of this method.By maximizing penal-ized empirical likelihood objective function,we obtain parameter estimator.We study the asymptotic property of estimator in theory and numerical simulations.This thesis is divided into three chapters,the main contents are as follows:The first chapter presents the background of the research and reviews the relevan-t knowledge and theory.Empirical likelihood and variable selection are introduced in detail.The main work of this paper is also listed.In the second chapter,penalized empirical likelihood for partially linear model is discussed when both parameter and nonparametric have measurement errors.We con-struct auxiliary random variable by the kernel estimation method,so the penalized em-pirical likelihood estimator is obtained.Theory and simulation studies prove our theory,that is,proposed estimator have consistency and oracle property.Finally,we consider the problem of hypothesis testing.The profiled penalized empirical likelihood ratio is asymptotically chi-square distribution.In the third chapter,based on appropriate auxiliary random variable,we propose pe-nalized empirical likelihood with adaptive lasso in high dimensional generalized linear models.Our main findings are that the extended penalized empirical likelihood has the oracle property and the asymptotic distribution of the test statistics constructed in the hy-pothesis test is chi-square distribution.Simulation studies and real data analysis indicate that the efficiency of the proposed penalized empirical likelihood estimator is encourag-ing.