Statistical Inference For Partially Linear Panel Data Models With Locally Stationary Regressors

Panel data is a kind of data that integrates cross-sectional data and time series,which has two dimensions.By establishing panel data models,we can make comprehensive use of sample information,which can not only analyze the differences between individuals,but also describe the dynamic changes of individuals.Panel data is an important research topic in modern econometrics.In this paper,we study the statistical inference for partially linear panel data models with locally stationary regressors,which allow individuals to be locally stationary in time.First,the differential profile likelihood method is used to estimate the unknown parameters of the models,and the consistency of estimators are given.Then,we use invariance principle to construct the uniform confidence band for nonparametric function.Finally,we carry out numerical simulation and real data analysis.The results show that the estimation method and uniform confidence band construction method proposed in this paper have good performance under finite sample.This article is organized as follows.Chapter 1,the partially linear panel data models with locally stationary regressors is proposed.The correlated knowledge about models and the main work of this paper are introduced.Chapter 2,we use the differential profile likelihood method to estimate the unknown parameters of the models.In chapter 3,we give some hypothetical conditions and the consistency of estimators.We further give the theoretical basis and the method for constructing uniform confidence band.Chapter 4,we present simulated examples to show its performance under the finite sample.Chapter 5,we present the real data analysis.The detailed proof process of the theorems we proposed in this paper is in chapter 6.