  We develop a novel procedure for constructing confidence bands for components
of a sparse additive model. Our procedure is based on a new kernel-sieve hybrid
estimator that combines two most popular nonparametric estimation methods in
the literature, the kernel regression and the spline method, and is of interest
in its own right. Existing methods for fitting sparse additive model are
primarily based on sieve estimators, while the literature on confidence bands
for nonparametric models are primarily based upon kernel or local polynomial
estimators. Our kernel-sieve hybrid estimator combines the best of both worlds
and allows us to provide a simple procedure for constructing confidence bands
in high-dimensional sparse additive models. We prove that the confidence bands
are asymptotically honest by studying approximation with a Gaussian process.
Thorough numerical results on both synthetic data and real-world neuroscience
data are provided to demonstrate the efficacy of the theory.
