We extend the varying coefficient functional linear model to the nonlinear model and propose a varying coefficient functional additive model. The proposed method can represent the relationship between functional predictors and a scalar response where the response depends on an exogenous variable.It captures the nonlinear structure between variables and also provides interpretable relationship of them. The model is estimated through basis expansions and penalized likelihood method, and then the tuning parameters included at the estimation procedure are selected by a model selection criterion. Simulation studies are provided to show the effectiveness of the proposed method. We also apply it to the analysis of crop yield data and then investigate how and when the environmental factor relates to the amount of the crop yield.
A novel generalized additive scalar-on-function regression model for partially observed multidimensional functional data: An application to air quality classification
Optimal Prediction in an Additive Functional Model
The functional generalized additive model (FGAM) provides a more flexible nonlinear functional regression model than the well-studied functional linear regression model. This paper restricts attention to the FGAM with identity link and additive errors, which we will call the additive functional model, a generalization of the functional linear model . This paper studies the minimax rate of convergence of predictions from the additive functional model in the framework of reproducing kernel Hilbert space . It is shown that the optimal rate is determined by the decay rate of the eigenvalues of a s…
Bayesian Functional Generalized Additive Models with Sparsely Observed Covariates
McLean等人（2013）最近提出了函数广义可加模型（FGAM），作为常见函数线性模型（FLM）的更灵活的替代方案，用于回归函数协变量的标量。在本文中，我们开发了一个贝叶斯版本的FGAM的高斯误差的情况下，单位链接功能。我们的方法允许函数协变量被稀疏地观察和测量，而McLean et al.（2013）的估计过程要求它们在规则网格上被无噪声地观察。我们认为这两个蒙特卡罗和变分贝叶斯方法拟合FGAM稀疏观测协变量。由于模型后验分布和全条件分布的复杂形式，标准蒙特卡罗和变分贝叶斯算法不能使用。我们使用的策略来处理更新的参数没有封闭形式的完整条件应该是独立的兴趣应用贝叶斯统计学家与非共轭模型。我们的数值研究表明，我们的算法的好处，首先使用标准技术恢复完整的轨迹，然后拟合一个功能回归模型的两步方法。在一个真实的数据分析中，我们的方法被应用到预测在网上拍卖网站eBay上拍卖的物品的收盘价。
