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.

我们提出了一种双引导程序，用于减少独立和同分布函数数据的描述性统计的置信区间中的覆盖误差。通过一系列蒙特卡罗模拟，我们比较了单自举程序和双自举程序的有限样本性能，用于估计独立和同分布函数数据的描述性统计量的分布。以更长的计算时间为代价，使用相同 bootstrap 方法的双 bootstrap 降低了置信水平误差，并提供了比单 bootstrap 更高的覆盖精度。以加拿大气象站数据集为例，双引导程序提供了一种工具，用于可视化功能数据的描述性统计数据的分布。