Title: On weak convergence of recovered functional data
Authors: Yoshikazu Terada - Osaka University; RIKEN (Japan) [presenting]
Masaki Sasaki - Osaka University (Japan)
Abstract: In functional data analysis, subjects are represented as smooth curves, and observed data consist of observations of random curves at discrete time points. In some cases, such as classification problems, we need to recover individual smooth curves from discretely observed data, and the properties of the recovered curves play important roles. We focus on the weak convergence of the empirical distribution of the recovered smooth curves. The existing results require the independence of recovered individual curves. When the data are observed on a dense grid of time points for each subject, we may recover the smooth curves independently. However, when data are observed not so densely, we often use the reconstruction method based on functional principal component analysis (FPCA). In this case, the recovered curves are not independent anymore. Thus, we establish the weak convergence of the empirical measure of the individual curves recovered by FPCA.