Resampling Techniques for Estimating the Distribution of Descriptive Statistics of Functional Data

Re-sampling methods for estimating the distribution of descriptive statistics of functional data are considered. Through Monte-Carlo simulations, we compare the performance of several re-sampling methods commonly used for estimating the distribution of descriptive statistics. We introduce two re-sampling methods that rely on functional principal component analysis, where the scores were randomly drawn from multivariate normal distribution and Stiefel manifold. Illustrated by one-dimensional Canadian weather station data and two-dimensional bone shape data, the re-sampling methods provide a way of visualizing the distribution of descriptive statistics for functional data.