The functional linear array model
The functional linear array model
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DOI：
10.1177/1471082x14566913
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发表时间：
2015-06-01
影响因子：
1
通讯作者：
Greven, Sonja
中科院分区：
文献类型：
--
作者：
Brockhaus, Sarah;Scheipl, Fabian;Greven, Sonja
函数线性阵列模型（FLAM）是函数回归模型的统一模型类，包括函数对标量、标量对函数和函数对函数回归。函数或标量响应的均值、中值、分位数以及广义加性回归模型作为特殊情况包含在该通用框架中。我们的实现具有多种协变量效应，例如分组变量、标量和函数协变量的线性、平滑和交互效应。通过将模型表示为广义线性阵列模型来实现计算效率。虽然数组结构需要一个公共网格来实现功能响应，但允许缺失值。使用增强算法进行估计，该算法允许大量协变量和自动的数据驱动模型选择。为了说明模型类的灵活性，我们使用了汽车生产树脂固化、化石燃料热值和加拿大气候数据（电子补充中的最后一个）的三个应用。这些分别需要标量上的函数、函数上的标量和函数上的函数回归模型，以及鲁棒回归、空间函数回归、模型选择和缺失调节等附加功能。我们的方法的实现在 R 附加包 FDboost 中提供。
The functional linear array model (FLAM) is a unified model class for functional regression models including function-on-scalar, scalar-on-function and function-on-function regression. Mean, median, quantile as well as generalized additive regression models for functional or scalar responses are contained as special cases in this general framework. Our implementation features a broad variety of covariate effects, such as, linear, smooth and interaction effects of grouping variables, scalar and functional covariates. Computational efficiency is achieved by representing the model as a generalized linear array model. While the array structure requires a common grid for functional responses, missing values are allowed. Estimation is conducted using a boosting algorithm, which allows for numerous covariates and automatic, data-driven model selection. To illustrate the flexibility of the model class we use three applications on curing of resin for car production, heat values of fossil fuels and Canadian climate data (the last one in the electronic supplement). These require function-on-scalar, scalar-on-function and function-on-function regression models, respectively, as well as additional capabilities such as robust regression, spatial functional regression, model selection and accommodation of missings. An implementation of our methods is provided in the R add-on package FDboost.