Functional Additive Models

• 成果类型: Article
• 署名作者: Mueller, Hans-Georg; Yao, Fang
• 署名单位: University of California System; University of California Davis; University of Toronto
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214508000000751
• 发表日期: 2008
• 页码: 1534-1544
• 关键词: GENERALIZED LINEAR-MODELS; regression

摘要

In commonly used functional regression models. the regression of it scalar or functional response oil the functional predictor is assumed to be linear. This means that the response is a linear function of the functional principal component scores of the predictor process. We relax the linearity assumption and propose to replace it by an additive structure. leading to it more widely applicable and much more flexible framework for functional regression models. The proposed functional additive regression models are Suitable for both scalar and functional response. The regularization needed for effective estimation of the regression parameter function is implemented through it projection on the eigenbasis of the covariance operator of the functional components in the model. The use of functional principal components in an additive rather than linear way leads to substantial broadening of the scope of functional regression models and emerges as a natural an additive rather than linear way leads to substantial broadening of the scope of functional regression models and emerges as a natural approach, because the uncorrelatedness of the functional principal components is shown to lead to a straightforward implementation of the functional additive model, based solely oil a sequence of one-dimensional smoothing, steps and without the need for backfitting. This facilitates the theoretical analysis. and we establish the asymptotic consistency of the estimates of the components of the functional additive model. We illustrate the empirical performance of the proposed modeling framework and estimation methods through simulation studies and in applications to gene expression time course data.