Generalised additive and index models with shape constraints
Journal of the Royal Statistical Society: Series B (Statistical Methodology)
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Chen, Y., & Samworth, R. (2015). Generalised additive and index models with shape constraints. Journal of the Royal Statistical Society: Series B (Statistical Methodology) https://doi.org/10.1111/rssb.12137
We study generalized additive models, with shape restrictions (e.g. monotonicity, convexity and concavity) imposed on each component of the additive prediction function. We show that this framework facilitates a non-parametric estimator of each additive component, obtained by maximizing the likelihood. The procedure is free of tuning parameters and under mild conditions is proved to be uniformly consistent on compact intervals. More generally, our methodology can be applied to generalized additive index models. Here again, the procedure can be justified on theoretical grounds and, like the original algorithm, has highly competitive finite sample performance. Practical utility is illustrated through the use of these methods in the analysis of two real data sets. Our algorithms are publicly available in the R package scar, short for shape-constrained additive regression.
Generalised additive models, Index models, Nonparametric maximum likelihood estimation, Shape constraints
Both authors are supported by the second author’s Engineering and Physical Sciences Research Fellowship EP/J017213/1.
Leverhulme Trust (PLP-2014-353)
External DOI: https://doi.org/10.1111/rssb.12137
This record's URL: https://www.repository.cam.ac.uk/handle/1810/249252
Creative Commons Attribution 4.0 International License
Licence URL: http://creativecommons.org/licenses/by/4.0/