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

Abstract

Resampling methods for estimating the distribution of descriptive statistics of functional data are considered. Through Monte-Carlo simulations, we compare the performance of several resampling methods commonly used for estimating the distribution of descriptive statistics. We introduce two resampling 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 resampling methods provide a way of visualizing the distribution of descriptive statistics for functional data.

Keywords:

• Bootstrap validity
• Functional mean
• Functional median
• Functional variance
• Smoothed bootstrap
• Trimmed functional mean

Mathematics Subject Classification:

• Primary 97K80
• Secondary 97K40