Partially Linear Functional Additive Models for Multivariate Functional Data
多元函数型数据的部分线性函数型可加模型AI 解读 ↓
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多元函数型数据的部分线性函数型可加模型
- 研究问题
- 如何同时利用标量与多个相关函数型预测变量解释标量响应，并在函数主成分数量增长时处理估计分数的测量误差？
- 方法与思路
- 作者用多元函数主成分刻画相关函数型预测变量，将分数效应设为可加项，并通过COSSO惩罚选择成分和正则化拟合。
- 材料陈述的贡献
- 摘要称在主成分数量发散时建立估计收敛速度，在可加成分数固定时给出部分线性系数的渐近分布，并展示作物产量预测。
- 阅读关注点
- 应核对主成分分数误差随阶数增加的控制、成分增长与平滑条件，以及渐近分布结果和产量预测比较的适用范围。
- 阅读边界
- 材料为稿件版本未注明的OpenAlex索引摘要，未给出具体速度、分布或预测指标；不同成分数量设定下的理论结论不能互换。
原文摘要
Raymond K. W. Wonga, Yehua Lib* http://orcid.org/0000-0002-5945-378X & Zhengyuan Zhuca Department of Statistics, Texas A&M University, College Station, TXb Department of Statistics, University of California, Riverside, CAc Department of Statistics & Statistical Laboratory, Iowa State University, Ames, IACONTACT Yehua Li yehuali@ucr.edu Department of Statistics, University of California, Riverside, CA 92521Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/r/JASA.Supplementary materials for this article are available online. Please go to www.tandfonline.com/r/JASA.ABSTRACTWe investigate a class of partially linear functional additive models (PLFAM) that predicts a scalar response by both parametric effects of a multivariate predictor and nonparametric effects of a multivariate functional predictor. We jointly model multiple functional predictors that are cross-correlated using multivariate functional principal component analysis (mFPCA), and model the nonparametric effects of the principal component scores as additive components in the PLFAM. To address the high-dimensional nature of functional data, we let the number of mFPCA components diverge to infinity with the sample size, and adopt the component selection and smoothing operator (COSSO) penalty to select relevant components and regularize the fitting. A fundamental difference between our framework and the existing high-dimensional additive models is that the mFPCA scores are estimated with error, and the magnitude of measurement error increases with the order of mFPCA. We establish the asymptotic convergence rate for our estimator, while allowing the number of components diverge. When the number of additive components is fixed, we also establish the asymptotic distribution for the partially linear coefficients. The practical performance of the proposed methods is illustrated via simulation studies and a crop yield prediction application. Supplementary materials for this article are available online.