Double bootstrapping for visualizing the distribution of descriptive statistics of functional data

We propose a double bootstrap procedure for reducing coverage error in the confidence intervals of descriptive statistics for independent and identically distributed functional data. Through a series of Monte Carlo simulations, we compare the finite sample performance of single and double bootstrap procedures for estimating the distribution of descriptive statistics for independent and identically distributed functional data. At the cost of longer computational time, the double bootstrap with the same bootstrap method reduces confidence level error and provides improved coverage accuracy than the single bootstrap. Illustrated by a Canadian weather station data set, the double bootstrap procedure presents a tool for visualizing the distribution of the descriptive statistics for the functional data.