Additive modelling of functional gradients

• 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: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asq056
• 发表日期: 2010
• 页码: 791805
• 关键词: Longitudinal Data; reaction norms; regression

摘要

We consider the problem of estimating functional derivatives and gradients in the framework of a regression setting where one observes functional predictors and scalar responses. Derivatives are then defined as functional directional derivatives that indicate how changes in the predictor function in a specified functional direction are associated with corresponding changes in the scalar response. For a model-free approach, navigating the curse of dimensionality requires the imposition of suitable structural constraints. Accordingly, we develop functional derivative estimation within an additive regression framework. Here, the additive components of functional derivatives correspond to derivatives of nonparametric one-dimensional regression functions with the functional principal components of predictor processes as arguments. This approach requires nothing more than estimating derivatives of one-dimensional nonparametric regressions, and thus is computationally very straightforward to implement, while it also provides substantial flexibility, fast computation and consistent estimation. We illustrate the consistent estimation and interpretation of the resulting functional derivatives and functional gradient fields in a study of the dependence of lifetime fertility of flies on early life reproductive trajectories.