Title: Simultaneous Confidence Band for Partially Linear Panel Data Models with Fixed Effects,
Abstract: In this paper, we construct the simultaneous confidence band (SCB) for the
nonparametric component in partially linear panel data models with fixed
effects. We remove the fixed effects, and further obtain the estimators of
parametric and nonparametric components, which do not depend on the fixed
effects. We establish the asymptotic distribution of their maximum absolute
deviation between the estimated nonparametric component and the true
nonparametric component under some suitable conditions, and hence the result
can be used to construct the simultaneous confidence band of the nonparametric
component. Based on the asymptotic distribution, it becomes difficult for the
construction of the simultaneous confidence band. The reason is that the
asymptotic distribution involves the estimators of the asymptotic bias and
conditional variance, and the choice of the bandwidth for estimating the second
derivative of nonparametric function. Clearly, these will cause computational
burden and accumulative errors. To overcome these problems, we propose a
Bootstrap method to construct simultaneous confidence band. Simulation studies
indicate that the proposed Bootstrap method exhibits better performance under
the limited samples.