  Statistical inference in high dimensional settings has recently attracted
enormous attention within the literature. However, most published work focuses
on the parametric linear regression problem. This paper considers an important
extension of this problem: statistical inference for high dimensional sparse
nonparametric additive models. To be more precise, this paper develops a
methodology for constructing a probability density function on the set of all
candidate models. This methodology can also be applied to construct confidence
intervals for various quantities of interest (such as noise variance) and
confidence bands for the additive functions. This methodology is derived using
a generalized fiducial inference framework. It is shown that results produced
by the proposed methodology enjoy correct asymptotic frequentist properties.
Empirical results obtained from numerical experimentation verify this
theoretical claim. Lastly, the methodology is applied to a gene expression data
set and discovers new findings for which most existing methods based on
parametric linear modeling failed to observe.

Methodology