Empirical Likelihood Testing And Effective Instrumental Variable Selection For Semi-Functional Partial Linear Models With Endogenous Covariates

With the improvement of computer storage capacity and data collection technology,data increasingly exists in the form of curves and images.Curve and image data are often referred to as functional data due to their infinite dimensional characteristics.Functional data is widely used in many fields such as meteorology,finance,medical treatment,and so on,which has attracted the attention of many scholars.There have been numerous theoretical studies and application developments surrounding functional data,including model studies on functional data,such as functional partial linear models,which are still ongoing.Functional partial linear models can depict infinite dimensional data such as curves and image forms,while retaining the advantages of semi parametric models,and are widely used in the field of econometrics.In practical research,some covariates are often accompanied by endogenous phenomena and produce endogenous bias.Therefore,this thesis conducts theoretical research based on a semi functional partial linear regression model with endogenous covariates.Firstly,after comparing many tests such as the section likelihood ratio test,an empirical likelihood ratio test with relatively simple test conditions is selected,and a model testing method is proposed based on it.Next,based on the least squares estimation,an auxiliary regression model is constructed,and combined with the penalty function,a regularized estimation process for identifying effective instrumental variables is proposed.In this research and analysis,empirical likelihood method is often used in nonparametric statistical inference,and empirical likelihood method does not need to estimate variance,thereby reducing the complexity of the estimation process.Therefore,firstly,instrumental variables are introduced to eliminate the endogenous problem of the model,kernel function method is used to process functional variables,and empirical likelihood method is used to construct test statistics for linear parameters of the model.A model testing method is proposed.Under the original hypothesis,it is theoretically proved that the proposed empirical likelihood ratio statistic asymptotically follows a central Chi square distribution.Secondly,by constructing an auxiliary regression model,a penalty least square estimation is established for a functional partial linear model with endogenous covariates.An effective tool variable identification method is proposed,and the estimated values of model parameters are given.Under some regularization conditions,it is proved that the estimator proposed in this thesis has consistency and sparsity.Finally,based on the theoretical research proposed in this article,the impact of foreign trade on economic growth in Chongqing is analyzed.Through variable identification,the bilateral trade degree is selected as an effective tool variable,and the tool variable model is introduced into the functional partial linear model.The simulation study shows that foreign trade has a significant promoting effect on economic growth.