Generalized additive and index models with shape constraints

作     者：Chen, Yining Samworth, Richard J. 

作者机构：Univ Cambridge Cambridge CB2 1TN England 

出 版 物：《JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY》 (皇家统计学会志，B辑：统计方法论)

年 卷 期：2016年第78卷第4期

页      面：729-754页

核心收录：

学科分类：0202[经济学-应用经济学] 02[经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 

基　　金：Engineering and Physical Sciences Research Fellowship [EP/J017213/1] EPSRC [EP/J017213/1] Funding Source: UKRI 

主　　题：Generalized additive models Index models Non-parametric maximum likelihood estimation Shape constraints 

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.