Surface Estimation, Variable Selection, and the Nonparametric Oracle Property.

TitleSurface Estimation, Variable Selection, and the Nonparametric Oracle Property.
Publication TypeJournal Article
Year of Publication2011
AuthorsStorlie, Curtis B., Howard D. Bondell, Brian J. Reich, and Hao Helen Zhang
JournalStat Sin
Date Published2011 Apr

Variable selection for multivariate nonparametric regression is an important, yet challenging, problem due, in part, to the infinite dimensionality of the function space. An ideal selection procedure should be automatic, stable, easy to use, and have desirable asymptotic properties. In particular, we define a selection procedure to be nonparametric oracle (np-oracle) if it consistently selects the correct subset of predictors and at the same time estimates the smooth surface at the optimal nonparametric rate, as the sample size goes to infinity. In this paper, we propose a model selection procedure for nonparametric models, and explore the conditions under which the new method enjoys the aforementioned properties. Developed in the framework of smoothing spline ANOVA, our estimator is obtained via solving a regularization problem with a novel adaptive penalty on the sum of functional component norms. Theoretical properties of the new estimator are established. Additionally, numerous simulated and real examples further demonstrate that the new approach substantially outperforms other existing methods in the finite sample setting.

Alternate JournalStat Sin
Original PublicationSurface estimation, variable selection, and the nonparametric oracle property.
PubMed ID21603586
PubMed Central IDPMC3095957
Grant ListP01 CA142538 / CA / NCI NIH HHS / United States
R01 CA085848 / CA / NCI NIH HHS / United States
R01 CA085848-10 / CA / NCI NIH HHS / United States