  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 visualising the distribution of the descriptive
statistics for the functional data.
