  We propose statistical inferential procedures for panel data models with
interactive fixed effects in a kernel ridge regression framework.Compared with
traditional sieve methods, our method is automatic in the sense that it does
not require the choice of basis functions and truncation parameters.Model
complexity is controlled by a continuous regularization parameter which can be
automatically selected by generalized cross validation. Based on empirical
processes theory and functional analysis tools, we derive joint asymptotic
distributions for the estimators in the heterogeneous setting. These joint
asymptotic results are then used to construct confidence intervals for the
regression means and prediction intervals for the future observations, both
being the first provably valid intervals in literature. Marginal asymptotic
normality of the functional estimators in homogeneous setting is also obtained.
Simulation and real data analysis demonstrate the advantages of our method.
