Bootstrap Methods for Canonical Correlation Analysis of Functional Data

Abstract

The bootstrap method is a very general resampling procedure for investigating the distributional property of statistics. In this paper, we present two bootstrap methods with the aim of studying the functional canonical components for functional data. The bootstrap I method constructs the bootstrap replications by resampling from the raw data, while the bootstrap II algorithm samples with replacement from the principal component scores. Simulation studies are conducted to examine the performance of the proposed bootstrap methods. The method is also applied to the motion analysis dataset, which consists of the angles formed by the hip and knee of each of 39 children over each child’s gait cycle. Numerical simulations and real data analysis show the good performance of both bootstrap methods for functional canonical correlation analysis. Moreover, as measured by the mean error and mean squared error, the bootstrap II algorithm performs better in approximating sample canonical components than the bootstrap I method.

Received: 23 August 2023 | Revised: 26 October 2023 | Accepted: 14 November 2023

Conflicts of Interest

The authors declare that they have no conflicts of interest to this work.

Data Availability Statement

Data available on request from the corresponding author upon reasonable request.