This paper studies linear reconstruction of partially observed functional data which are recorded on a discrete grid. We propose a novel estimation approach based on approximate factor models with increasing rank. Whereas alternative reconstruction procedures commonly involve some preliminary smoothing, our method separates the signal from noise and reconstructs missing fragments at once. We establish uniform convergence rates of our estimator and introduce a new method for constructing simultaneous prediction bands for the missing trajectories. A simulation study examines the performance of the proposed methods in finite samples. Finally, a real data application of temperature curves demonstrates that our theory provides a simple and effective method to recover missing fragments.

翻译：本文研究在离散网格上记录的部分观测函数型数据的线性重构问题。我们提出了一种基于递增秩近似因子模型的新型估计方法。不同于常用预平滑处理的替代性重构程序，本文方法能同时分离信号与噪声并重建缺失片段。我们建立了估计量的均匀收敛速率，并引入了一种为缺失轨迹构建同步预测带的新方法。模拟研究考察了所提方法在有限样本下的表现。最后，通过气温曲线的真实数据应用表明，本文理论提供了恢复缺失片段的简便有效方法。