A0803
Title: Covariance test for discretely observed functional data: When and how it works
Authors: Yang Zhou - Beijing Normal University (China) [presenting]
Abstract: For covariance tests in functional data analysis, the existing methods are only developed for fully observed curves, while in reality, one observes such trajectories discretely with noise. To bridge this gap, a projection-based test statistic is constructed and allows the number of estimated eigenfunctions potentially to grow with sample size, leading to a consistent nonparametric test with challenges arising from the concurrence of the diverging truncation and discretized observations. The pooling method and sample-splitting strategy are used to attain the test statistic and derive its asymptotic Chi-squared null distribution facilitated by advancing the perturbation bound of estimated principal components. The theoretic analysis reveals an interesting connection between the permissible truncation level, the sampling frequency and the sample size. It is shown that the asymptotic null distribution remains valid for different allowable ranges of truncation level, and when the sampling frequency reaches a certain magnitude of the sample size, it behaves as if the functions are fully observed. This investigation provides for the first time the theoretical justification and practical guidance on when and how the covariance test procedure works by allowing growing truncation levels for discretely observed functional data that range from "sparse" to "dense" paradigms.
