Variable Selection For Varying Coefficient Model With Interactive Fixed Effects

The varying coefficient panel data model with interactive fixed effects is an important extension of the traditional fixed effects model,the model is more adaptive and has stronger explanation ability.It has been widely used in econometrics,biomedicine and other fields.Variable selection solves various problems caused by researchers including as many explanatory variables as possible in order to avoid missing important influencing factors.Although interactive effects,the varying coefficient model and variable selection have well developed,there is no article about variable selection in varying coefficient model with interactive effect,So the paper studies the variable selection problem of varying coefficient model panel data with interactive fixed effects.The research contents of this paper is as follows: Firstly,the varying coefficient of the model is expanded by B-spline,the interaction effect in the model is eliminated by projection matrix,the model does not contain interactive terms in form and becomes panel data linear model.Secondly,the SCAD penalty function is used to select variables of the model and the data-driven method is used to select the required adjustment parameters to ensure the sparseness of the model and the smoothness of the function curve.Considering that the transformed model does not contain interactive terms,but there is still have common factor ,we construct the formula of pure factor and get the estimation expression of .The estimation expression of is obtained by principal component analysis.The selection of non-zero function coefficients,the estimation of non-zero function coefficients and the estimation of are completed by iterative method.Thirdly,we find that the SCAD penalty function is better than Lasso through the numerical simulation method of variable selection under the limited sample.And no matter which variable selection method,the introduction of interactive effects in the model is better than the fitting effect of ignoring interactive effects directly.Then we prove that the necessity of introducing interaction effect into the model and the validity of variable selection.Finally,we prove the consistency of coefficient function estimation under the proper regular condition.