Statistical inference in the high dimensional settings has recently attractedenormous attention from the literature. However, most of the published workfocuses on the parametric linear regression problem. This paper considers animportant extension of this problem: statistical inference for high dimensionalsparse nonparametric additive models. To be more specific, this paper developsa methodology for constructing a probability density function on the set of allcandidate models. This methodology can also be applied to construct confidenceintervals for the model parameters and confidence bands for the additivefunctions. This methodology is derived using the generalized fiducial inferenceframework. It is shown that results produced by the proposed methodology enjoycorrect asymptotic frequentist property. Empirical results obtained fromnumerical experimentation verify this theoretical claim. Lastly, themethodology is applied to a gene expression data set and discovered newfindings for which most existing methods based on parametric linear modelingfailed to observe.
展开▼
