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Generalized additive and index models with shape constraints

Chen, Yining ORCID: 0000-0003-1697-1920 and Samworth, Richard J. (2016) Generalized additive and index models with shape constraints. Journal of the Royal Statistical Society. Series B: Statistical Methodology, 78 (4). 729 - 754. ISSN 1369-7412

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Identification Number: 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.

Item Type: Article
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Additional Information: © 2015 The Authors © CC BY 4.0
Divisions: Statistics
Subjects: Q Science > QA Mathematics
Date Deposited: 16 Mar 2016 10:39
Last Modified: 12 Jun 2024 18:12

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