Covariance estimation error of incomplete functional data under RKHS framework

•Global estimation error of the covariance function is obtained by using functional data fragments.•A theorem realizes the intersection and intercommunication of incomplete functional data and reproducing kernel Hilbert space (RKHS).•The N resolution patched (N-rp) method is improved by significantly reducing its computational complex. In recent years, functional data analysis (FDA) and reproducing kernel Hilbert space (RKHS) are frequently encountered in various applications. However, employing the RKHS framework to study the covariance of incomplete functional data is rare. In this paper, we consider 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 function 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 existing 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.