Abstract
SUMMARY In nonparametric multivariate regression analysis, we seek methods to reduce the dimensionality of the regression function to bypass the difficulty caused by the curse of dimensionality. The original additive models approximate a regression function by additive univariate functions, which overcome successfully the difficulty caused by the curse of dimensionality and have a clear interpretation. But since they ignore any interactions between regressors they are not sufficiently flexible to cope with the case where interactions are of concern. In this paper, we study interactive models in which the regression function is approximated by an analysis-of-variance-type function. The models retain all the advantages of the original additive models but are much more flexible. We study ways of fitting an interactive model by the smoothing spline method. We relate the well-known backfitting algorithm to a typical penalized least squares problem in the context of the smoothing spline method. We develop a non-standard method based on bootstrap methodology for model selection in the interaction spline modelling.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Journal of the Royal Statistical Society Series B: Statistical Methodology
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.