Covariance estimation error of incomplete functional data under RKHS framework

In recent years, functional data analysis (FDA) and reproducing kernel Hilbert space (RKHS) are frequently encountered in various applications. However, employing the RKHS frame-work to study the covariance of incomplete functional data is rare. In this paper, we con-sider the global estimation error of the covariance function obtained by fragment data. Our theorem is built on the connection between functional data and RKHS, by using the covariance function as the reproducing kernel. We take the mean square integrability of functional data into consideration, and ease the previous restrictions of covariance func-tion and observation area. Simulation results show the veracity of our theoretical finding by comparing the error of two kinds of functional data in covariance estimation. The exist-ing N resolution patched (N-rp) method to estimate covariance in a local observation area has been improved, resulting in a considerable reduction in computing costs. (c) 2022 Elsevier Inc. All rights reserved.

Automated summary

In recent years, functional data analysis (FDA) and reproducing kernel Hilbert space (RKHS) have been commonly used in various applications. However, the application of RKHS framework to study the covariance of incomplete functional data is rare. This paper investigates the global estimation error of the covariance function obtained from fragmented data, considering the connection between functional data and RKHS. The simulation results demonstrate the validity of the theoretical findings by comparing the estimation errors of two types of functional data.