Reiss Philip T, Miller David L, Wu Pei-Shien, Hua Wen-Yu
Department of Child and Adolescent Psychiatry and Department of Population Health, New York University, USA and Department of Statistics, University of Haifa, Israel.
Integrated Statistics, Woods Hole, Massachusetts, USA and Centre for Research into Ecological and Environmental Modelling and School of Mathematics and Statistics, University of St Andrews, St Andrews, Scotland, United Kingdom.
J Comput Graph Stat. 2017;26(3):569-578. doi: 10.1080/10618600.2016.1217227. Epub 2016 Aug 2.
A number of classical approaches to nonparametric regression have recently been extended to the case of functional predictors. This paper introduces a new method of this type, which extends intermediate-rank penalized smoothing to scalar-on-function regression. In the proposed method, which we call , one regresses the response on leading principal coordinates defined by a relevant distance among the functional predictors, while applying a ridge penalty. Our publicly available implementation, based on generalized additive modeling software, allows for fast optimal tuning parameter selection and for extensions to multiple functional predictors, exponential family-valued responses, and mixed-effects models. In an application to signature verification data, principal coordinate ridge regression, with dynamic time warping distance used to define the principal coordinates, is shown to outperform a functional generalized linear model.
最近，一些经典的非参数回归方法已扩展到函数型预测变量的情况。本文介绍了一种此类新方法，它将中间秩惩罚平滑扩展到函数对标量的回归。在所提出的方法（我们称之为 ）中，人们将响应变量对由函数型预测变量之间的相关距离定义的主坐标进行回归，同时应用岭惩罚。我们基于广义相加模型软件的公开可用实现，允许快速进行最优调优参数选择，并可扩展到多个函数型预测变量、指数族值响应变量以及混合效应模型。在一个签名验证数据的应用中，使用动态时间规整距离来定义主坐标的主坐标岭回归被证明优于函数型广义线性模型。
