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Generalized additive and index models with shape constraints
Author(s) -
Chen Yining,
Samworth Richard J.
Publication year - 2016
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12137
Subject(s) - convexity , additive model , monotonic function , generalized additive model , estimator , mathematics , parametric statistics , component (thermodynamics) , mathematical optimization , function (biology) , additive function , parametric model , algorithm , computer science , statistics , mathematical analysis , physics , evolutionary biology , biology , financial economics , economics , thermodynamics
Summary 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.