  In this paper, we propose a robust estimation and inferential method for
high-dimensional panel data models. Specifically, (1) we investigate the case
where the number of regressors can grow faster than the sample size, (2) we pay
particular attention to non-Gaussian, serially and cross-sectionally correlated
and heteroskedastic error processes, and (3) we develop an estimation method
for high-dimensional long-run covariance matrix using a thresholded estimator.
  Methodologically and technically, we develop two Nagaev-types of
concentration inequalities: one for a partial sum and the other for a quadratic
form, subject to a set of easily verifiable conditions. Leveraging these two
inequalities, we also derive a non-asymptotic bound for the LASSO estimator,
achieve asymptotic normality via the node-wise LASSO regression, and establish
a sharp convergence rate for the thresholded heteroskedasticity and
autocorrelation consistent (HAC) estimator.
  Our study thus provides the relevant literature with a complete toolkit for
conducting inference about the parameters of interest involved in a
high-dimensional panel data framework. We also demonstrate the practical
relevance of these theoretical results by investigating a high-dimensional
panel data model with interactive fixed effects. Moreover, we conduct extensive
numerical studies using simulated and real data examples.
