论文标题
基于集成预测的功能线性模型的合适性测试
Goodness-of-fit tests for functional linear models based on integrated projections
论文作者
论文摘要
功能线性模型是评估功能性或标量性质的两个随机变量之间关系的最基本工具之一。该贡献提出了对功能线性模型的拟合优点测试，其功能响应巧妙地适应了功能/标量响应/预测因子。特别是，新的合适性测试扩展了标量响应的先前建议。测试统计量基于方便的正则估计器，易于计算，并通过有效的引导重新采样进行校准。通过新颖的数据应用程序介绍并说明了一个图形诊断工具，可用于可视化与模型的偏差。 R软件包GOFFDA实现了所提出的方法，并允许数据应用程序的可重复性。
Functional linear models are one of the most fundamental tools to assess the relation between two random variables of a functional or scalar nature. This contribution proposes a goodness-of-fit test for the functional linear model with functional response that neatly adapts to functional/scalar responses/predictors. In particular, the new goodness-of-fit test extends a previous proposal for scalar response. The test statistic is based on a convenient regularized estimator, is easy to compute, and is calibrated through an efficient bootstrap resampling. A graphical diagnostic tool, useful to visualize the deviations from the model, is introduced and illustrated with a novel data application. The R package goffda implements the proposed methods and allows for the reproducibility of the data application.
