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

TL;DR

This paper introduces a double bootstrap method to improve the accuracy of confidence intervals for descriptive statistics of functional data, demonstrated through simulations and a weather data case study.

Contribution

It presents a novel double bootstrap approach that reduces coverage error in confidence intervals for functional data, outperforming single bootstrap methods.

Findings

Double bootstrap reduces confidence level error.

Improved coverage accuracy over single bootstrap.

Effective visualization tool for functional data distributions.

Abstract

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.