# Simultaneous Confidence Band for Partially Linear Panel Data Models with Fixed Effects

## TL;DR

This paper develops a bootstrap-based method to construct simultaneous confidence bands for the nonparametric component in partially linear panel data models with fixed effects, addressing computational and bias estimation challenges.

## Contribution

It introduces a bootstrap approach for SCB construction in partially linear panel models, removing fixed effects and overcoming bias and variance estimation issues.

## Key findings

- Bootstrap method outperforms traditional methods in simulations
- Provides reliable confidence bands with limited sample sizes
- Addresses computational complexity in SCB construction

## 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.