Partially Linear Functional Additive Models for Multivariate Functional Data
Partially Linear Functional Additive Models for Multivariate Functional Data
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DOI：
10.1080/01621459.2017.1411268
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发表时间：
2018-06
影响因子：
3.7
通讯作者：
R. K. Wong;Yehua Li;Zhengyuan Zhu-
中科院分区：
文献类型：
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作者：
R. K. Wong;Yehua Li;Zhengyuan Zhu-
我们研究了一类部分线性泛函加性模型（PLFAM），它通过多变量预测器的参数效应和多变量泛函预测器的非参数效应来预测标量响应。我们使用多变量功能主成分分析（mFPCA）对交叉相关的多个功能预测因子进行了联合建模，并将主成分得分的非参数效应作为PLFAM中的附加成分进行了建模。为了解决函数数据的高维性质，我们让mFPCA组件的数量随样本量发散到无穷大，并采用组件选择和平滑算子（COSSO）惩罚来选择相关组件并正则化拟合。我们的框架与现有的高维加性模型的一个根本区别是，mFPCA分数的估计是有误差的，并且测量误差的大小随着mFPCA的阶数而增加。在允许分量数目发散的情况下，我们建立了估计量的渐近收敛速率。当加性分量数目一定时，我们也建立了部分线性系数的渐近分布。通过模拟研究和作物产量预测应用，说明了所提方法的实际性能。本文的补充材料可在网上获得。
ABSTRACT We 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.