The Experience Likelihood And Punishment Experience Likelihood Under The Two Models In Longitudinal Data

Longitudinal data refers to the survey data of the same cross-sectional unit in different periods.Generally,the observed values in different individuals are independent,and the ob-served values in the same individual are correlated.Therefore,the longitudinal data has the characteristics of both the time series data and the cross-section data.In practical research,longitudinal data often appears in biological,medical,social and economic fields.For ex-ample,it is used to study the rapid fluctuations of behaviors,thoughts and emotions in social personality and clinical psychology and to explore predictive factors of certain diseases in medicine.Therefore,the study of longitudinal data has important practical significance.Generalized linear model was proposed to overcome the shortcomings of the linear model.Its variable can be discrete or continuous,and the distribution of response variable is exponential family distribution.The covariates and response variable have a effect through the link function.Therefore,compared with the linear model,the generalized linear model has more extensive application and better properties,such as fitting the count data.In addi-tion,partially linear model is an important statistical model,which is composed of two parts:parametric and nonparametric parts.Because partially linear model can fit the practical data well,more and more attention has been paid by statisticians in recent years.Empirical likelihood is an nonparametric statistical method.It combines,the reliability of nonparametric methods with the flexibility and effectiveness of the likelihood methods.At the same time,empirical likelihood has the advantages of nonparametric version of Wilk'theorem and Bartlett correction.In the beginning of a longitudinal study,often a large number of covariates are suspected to have influence on the response variables.Because not all covariates have significant influence,a variable selection procedure like penalized empirical likelihood should be considered.With the development of science and technology,the high dimensional data grows rapidly in the world,so the penalized empirical likelihood method has been widely used in the research of various practical problems.This paper mainly studies the statistical properties of the penalized empirical likelihood for high-dimensional generalized linear models and empirical likelihood for partially linear errors-in-variables models.The thesis is divided into three chapters,and the main contents are as follows:In the first chapter,we introduce the research background of this paper.Then two kinds of models:generalized linear models and partially linear models are gave.The em-pirical likelihood and the penalty variable selection method are discussed.Finally,the main contents of this paper are briefly introduced.In the second chapter,the penalized empirical likelihood estimation and its asymptotic properties are obtained by penalized empirical likelihood method.The method can be used for variable selection and parameter estimation,simultaneously.At the same time,based on the hypothesis testing problem of parameter,we propose the penalized empirical loga-rithmic likelihood ratio testing statistic and prove the statistic converges to the chi-square distribution.In the third chapter,under the partially linear model with the measurement errors in the parametric and the nonparametric parts,we introduce the unbiased auxiliary vector to construct the empirical logarithmic likelihood ratio function and obtain the limiting distri-bution of empirical logarithmic likelihood ratio function.At the same time,the maximum empirical likelihood estimator,generalized least square estimator and modified weighted least square estimator converging to the normal distribution is proved.