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- Title
Precise Tensor Product Smoothing via Spectral Splines.
- Authors
Helwig, Nathaniel E.
- Abstract
Tensor product smoothers are frequently used to include interaction effects in multiple nonparametric regression models. Current implementations of tensor product smoothers either require using approximate penalties, such as those typically used in generalized additive models, or costly parameterizations, such as those used in smoothing spline analysis of variance models. In this paper, I propose a computationally efficient and theoretically precise approach for tensor product smoothing. Specifically, I propose a spectral representation of a univariate smoothing spline basis, and I develop an efficient approach for building tensor product smooths from marginal spectral spline representations. The developed theory suggests that current tensor product smoothing methods could be improved by incorporating the proposed tensor product spectral smoothers. Simulation results demonstrate that the proposed approach can outperform popular tensor product smoothing implementations, which supports the theoretical results developed in the paper.
- Subjects
TENSOR products; SPLINES; ANALYSIS of variance; REGRESSION analysis; PARAMETERIZATION
- Publication
Stats, 2024, Vol 7, Issue 1, p34
- ISSN
2571-905X
- Publication type
Article
- DOI
10.3390/stats7010003