SCAD-penalised generalised additive models with non-polynomial dimensionality
In this article, we study the (group) smoothly clipped absolute deviation (SCAD) estimator in the estimation of generalised additive models. The SCAD penalty, proposed by Fan and Li [(2001) ‘Variable Selection via Nonconcave Penalised Likelihood and Its Oracle Properties’, Journal of the American...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2013
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/98192 http://hdl.handle.net/10220/17090 |
| Summary: | In this article, we study the (group) smoothly clipped absolute deviation (SCAD) estimator in the estimation
of generalised additive models. The SCAD penalty, proposed by Fan and Li [(2001) ‘Variable Selection via
Nonconcave Penalised Likelihood and Its Oracle Properties’, Journal of the American Statistical Association
96(456), 1348–1360], has many desirable properties including continuity, sparsity and unbiasedness.
For high-dimensional parametric models, it has only recently been shown that the SCAD estimator can
deal with problems with dimensions much larger than the sample size. Here, we show that the SCAD
estimator can be successfully applied to generalised additive models with non-polynomial dimensionality
and our study represents the first such result for the SCAD estimator in nonparametric problems, as far
as we know. In particular, under suitable assumptions, we theoretically show that the dimension of the
problem can be close to exp{nd/(2d+1)}, where n is the sample size and d is the smoothness parameter of
the component functions. Some Monte Carlo studies and a real data application are also presented. |
|---|