Statistical Inference Of Semiparametric Panel Data Model Under Restricted Condition

Parametric regression model refers to a certain relationship between the explanatory variable and the explained variable.In practical analysis,if one blindly assumes the form of the relationship between variables,it may lead to errors or even completely opposite conclusions.With the increasing number of complex data,it has become inappropriate to analyze complex relationships between data in specific forms.Non parametric regression models are models that rely on data rather than subjective assumptions.However,when the dimensions of explanatory variables are higher,the model will face the problem of "dimensionality disaster"."Dimension disaster" refers to the phenomenon that the amount of computation exponentially increases as the dimension increases.Therefore,statisticians combine the two types of models to form a semi parametric model,but it is not a simple superposition of the two types of models.The semi parametric model has stronger adaptability than individual parametric or non-parametric models.In recent years,with the continuous growth of available panel data,the research on panel data models has become more practical.Panel data is a collection of observations made by different individuals at different time nodes.It combines the characteristics of cross sectional data and time series data to better infer the laws of multiple individuals changing over time.There are also individual differences in panel data,and individual effects will be introduced to address the issue of individual differences in panel data analysis.When there is some correlation between individual effects and explanatory variables,it is called a fixed effect.In practical applications,statistical models are always restricted by various situations.To solve this problem,this article introduces specific and simple equality restriction,and then conducts statistical inference to make the semi parametric panel data model more reasonable and adapt to actual needs.This article first introduces the research background and significance of semi-varing coefficient panel data models with fixed effects under restricted conditions,as well as the current research results and context of semi parametric panel data models at home and abroad,and briefly summarizes the research content of this article.Secondly,it explains how to infer the semi-varing coefficient panel data model with fixed effects under the condition of additional equality restricteds in the parameter section.Firstly,the profile least squares method is used to infer the unrestricted estimators of the parametric and nonparametric parts,and then the restricted conditions are taken into account in the model by constructing an auxiliary function.By making the derivative of the auxiliary function equal to 0,the restricted estimators of the parametric and nonparametric parts,and the restricted estimators of the error variance function can be obtained.Finally,it is proved that the obtained restricted estimators conform to the asymptotic normal distribution.Once again,considering that no matter what statistical method will bring measurement errors,the estimation results of the statistical model may deviate.Therefore,measurement errors are added to both the parametric and nonparametric parts,and restricted estimators corrected for the parametric and nonparametric parts are given.It is proved that the obtained restricted estimators conform to the asymptotic normal distribution.Finally,considering that as the panel dataset contains more and more information,the possibility of multicollinearity among variables increases.If the multicollinearity problem is not considered,the estimation results will have errors.Therefore,by using ridge estimation to eliminate the multicollinearity problem between variables,we finally obtain the restricted ridge estimators for parametric and nonparametric parts,and study the properties of the restricted ridge estimators for parametric parts.