Journal
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
Volume 78, Issue 4, Pages 729-754Publisher
OXFORD UNIV PRESS
DOI: 10.1111/rssb.12137
Keywords
Generalized additive models; Index models; Non-parametric maximum likelihood estimation; Shape constraints
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Funding
- Engineering and Physical Sciences Research Fellowship [EP/J017213/1]
- EPSRC [EP/J017213/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/J017213/1] Funding Source: researchfish
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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.
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