Abstract In this paper, we consider the estimation and inference in partially functional linear regression with multiple functional covariates. We estimate the parameters and the slope functions by using functional principal component analysis (FPCA) approach to each functional covariate; establish the asymptotic distribution for the proposed estimators and investigate the semiparametric efficiency. We derive the rates of convergence for the estimators of the slope functions, and prove that the rates are optimal. We also develop a linear hypothesis test for the parametric component, and construct confidence bands centered at FPCA-based estimator for the slope functions and verify its asymptotic validity. The performance of the proposed procedures is illustrated via simulation studies and an analysis of a diffusion tensor imaging data application.

中文翻译：

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具有多个函数协变量的部分函数线性回归的估计和推理

摘要 在本文中，我们考虑了具有多个函数协变量的部分函数线性回归中的估计和推理。我们通过对每个函数协变量使用函数主成分分析（FPCA）方法来估计参数和斜率函数；为建议的估计量建立渐近分布并研究半参数效率。我们推导出斜率函数估计量的收敛速度，并证明收敛速度是最优的。我们还为参数组件开发了一个线性假设检验，并构建了以基于 FPCA 的斜率函数估计器为中心的置信带，并验证其渐近有效性。通过模拟研究和扩散张量成像数据应用的分析说明了所提出程序的性能。