Generalized additive and index models with shape constraints

• 成果类型: Article
• 署名作者: Chen, Yining; Samworth, Richard J.
• 署名单位: University of Cambridge
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12137
• 发表日期: 2016
• 页码: 729-754
• 关键词: maximum-likelihood-estimation; multivariate convex regression; log-concave density; monotonic regression; isotonic regression; inference; algorithm; selection; Consistency; uniqueness

摘要

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.