Empirical Likelihood For Semiparametric Panel Data Models With Fixed Effects

Panel data refers to a portion of an individual(individual,family,business or Country,etc.)in a period of time a variable consisting of the observations dimensional data set.Panel data contains observations on two phenomena observed over multiple time periods for each individual.From the cross-section view,panel data is composed of a number of indi-viduals in a certain point section observation.And from the individual to see each individual is a time series.Time series and cross-sectional data are special cases of panel data that are in one-dimension only.Panel data are sometimes treated as cross-sections over time or pooled cross-section time-series data.Empirical research in economics has been enriched by the availability of panel data.With the increased availability of panel da-ta,both theoretical and applied work in panel data analysis have become more popular in the recent years.Analysis of panel data sets has various advantages over that of pure cross sectional or time series data sets.Panel data usually cover individu-al units sampled from different backgrounds and with different individual characteristics so that an abiding feature of the data is its heterogeneity,much of which is simply unobserved.Panel data provide researchers a flexible way to model both heterogeneity among cross sectional units and possible structural changes over time.The model we studied is a semiparametric model.Semiparametric model combines the flexibility of nonparametric regression and parsimo-ny of linear regression.The models are important and applied widely in economic,biological and medical studies.In this thesis,we study the empirical likelihood for semiparametric panel data models with fixed ef-fects.We mainly use the empirical likelihood method proposed by Owen(1988,1990).There are several nice advantages for empirical likelihood.the empirical likelihood regions are shaped completely by the sample,Bartlett correctable,range preserving and transformation respecting.So,the empirical likelihood method has been paid great attention by statis-ticians and economists and has received widely researches and applica-tions.Many researchers have applied the empirical likelihood method to various models and fields.For high-dimensional linear models,Tang and Leng(2010)and Leng and Tang(2012)propose a penalty empirical likelihood for parameter estimation and variable selection,and show that penalized empirical likelihood has the oracle property.The chapters are as follows:The first chapter is introduction,we state research background and research significance.we demonstrate the rationality and feasibility of the subject selection from the perspective of models and problems.In ad-dition,we briefly describing the research status of semi-parametric panel data models with fixed effects.At last,the main content of this disserta-tion are proposed.the research methods,research context and the main innovative points are summarized.In chapter 2,we consider a partially linear panel data models with fixed effects.In order to accommodate the within-group correlation,we apply the block empirical likelihood procedure to partially linear pan-el data models with fixed effects,and prove a nonparametric version of Wilks' theorem which can be used to construct the confidence region for the parametric.By the block empirical likelihood ratio function,the max-imum empirical likelihood estimator of the parameter is defined and the asymptotic normality is shown.A simulation study and a real data ap-plication are undertaken to assess the finite sample performance of our proposed method.the confidence regions construction for the parameter-s of interest in the partially linear regression model with linear process errors under martingale difference is studied.It is shown that the adjust-ed empirical log-likelihood ratio at the true parameters is asymptotical-ly chi-squared.A simulation study indicates that the adjusted empirical likelihood works better than a normal approximation-based approach.In chapter 3,we consider the statistical inference for the partially lin-ear panel data models with fixed effects.We focus on the case where some covariates are measured with additive errors.We propose a mod-ified profile least squares estimator of the regression parameter and the nonparametric components.The asymptotically normality for the para-metric component and the rate of convergence for the nonparametric component are established.Consistent estimations of the error variance are also developed.In addition,we introduce the profile likelihood ra-tio(PLR)test and then demonstrate that it follows an asymptotically ?2 distribution under the null hypothesis.We conduct simulation studies to demonstrate the finite sample performance of our proposed method and we also present an illustrative empirical application.In chapter 4,For the high-dimensional partially linear panel data models with fixed effects where covariates are measured with additive er-rors,we,in this chapter,propose a modified profile least squares estimator of the regression parameter and maximum empirical likelihood estimator of the regression parameter.At the same time,based on penalized em-pirical likelihood(PEL)approach,the parameter estimation and variable selection of the model are investigated,the proposed PEL estimators are shown to possess the oracle property.Also,we introduce the PEL ratio statistic to test a linear hypothesis of the parameter and prove it follows an asymptotically chi-square distribution under the null hypothesis.We conduct simulation studies to demonstrate the finite sample performance of our proposed method and we also present an illustrative empirical ap-plication.In chapter 5,The empirical likelihood inference for semi-varying co-efficient models for panel data with fixed effects is investigated in this paper.We propose an empirical log-likelihood ratio function for the re-gression parameters in the model under a-mixing condition.The empir-ical log-likelihood ratio is proven to be asymptotically chi-squared.We also obtain the maximum empirical likelihood estimator of the parame-ters of interest,and prove that it is the asymptotically normal under some suitable conditions.A simulation study and a real data application are un-dertaken to assess the finite sample performance of our proposed method.In chapter 6,The empirical likelihood inference for time-varying co-efficient models for panel data with fixed effects is investigated in this paper.We propose an empirical log-likelihood ratio function for the re-gression parameters in the model under ?-mixing condition.The em-pirical log-likelihood ratio is proven to be asymptotically standard chi-squared.A simulation study indicates that,compared with a normal approximation-based approach,the proposed method described herein works better in terms of coverage probabilities.Finally,in chapter 7,the research and main innovative points are briefly summarized,and some problems which need to be further per-fected and studied are pointed.