An empirical likelihood check with varying coefficient fixed effect model with panel data

Semiparametric models are often used to analyze panel data for a good trade-off between parsimony and flexibility. In this paper, we investigate a fixed effect model with a possible varying coefficient component. On the basis of empirical likelihood method, the coefficient functions are estimated as well as their confidence intervals. The estimation procedures are easily implemented. An important problem of the statistical inference with the varying coefficient model is to check the constant coefficient about the regression functions. We further develop checking procedures by constructing empirical likelihood ratio statistics and establishing the Wilks theorems. Finally, some numerical simulations and a real data analysis is presented to assess the finite sample performance.