Testing the Equality of Covariance Operators in Functional Samples

TL;DR

This paper introduces a robust statistical test to compare the covariance structures of two functional data samples, with proven asymptotic properties and demonstrated effectiveness through simulations and real data application.

Contribution

It presents a novel chi-square based test for equality of covariance operators in functional data, including detailed asymptotic analysis and practical validation.

Findings

Test statistic follows a chi-square distribution asymptotically.

The test performs well in finite samples as shown by simulations.

Application to fruit fly data demonstrates practical utility.

Abstract

We propose a robust test for the equality of the covariance structures in two functional samples. The test statistic has a chi-square asymptotic distribution with a known number of degrees of freedom, which depends on the level of dimension reduction needed to represent the data. Detailed analysis of the asymptotic properties is developed. Finite sample performance is examined by a simulation study and an application to egg-laying curves of fruit flies.