Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series

IRTG1792DP2018 002

Nonparametric Variable Selection and Its Application to Additive Models

Zheng-Hui Feng
Lu Lin
Ruo-Qing Zhu
Li-Xing Zhu

For multivariate nonparametric regression models, existing variable selection
methods with penalization require high-dimensional nonparametric approximations
in objective functions. When the dimension is high, none of methods with penalization
in the literature are readily available. Also, ranking and screening approaches
cannot have selection consistency when iterative algorithms cannot be used due to
inefficient nonparametric approximation. In this paper, a novel and easily implemented
approach is proposed to make existing methods feasible for selection with
no need of nonparametric approximation. Selection consistency can be achieved.
As an application to additive regression models, we then suggest a two-stage procedure
that separates selection and estimation steps. An adaptive estimation to
the smoothness of underlying components can be constructed such that the consistency
can be even at parametric rate if the underlying model is really parametric.
Simulations are carried out to examine the performance of our method, and a real
data example is analyzed for illustration.

Adaptive estimation; non-parametric additive model; purely nonparametric
regression; variable selection