Homogeneity Test for Functional Data based on Data-Depth Plots

TL;DR

This paper introduces a new homogeneity test for functional data using data depth plots, generalizing Q-Q plots, with bootstrap-based statistics that outperform existing methods in simulations and real data applications.

Contribution

It proposes a novel homogeneity test for functional data based on DD-plots, extending univariate Q-Q plots, with improved size and power over existing tests.

Findings

The test has better finite-sample size and power than existing methods.

Bootstrap techniques effectively estimate the test statistic distributions.

The method provides consistent results on real heterogeneous data samples.

Abstract

One of the classic concerns in statistics is determining if two samples come from thesame population, i.e. homogeneity testing. In this paper, we propose a homogeneitytest in the context of Functional Data Analysis, adopting an idea from multivariatedata analysis: the data depth plot (DD-plot). This DD-plot is a generalization of theunivariate Q-Q plot (quantile-quantile plot). We propose some statistics based onthese DD-plots, and we use bootstrapping techniques to estimate their distributions.We estimate the finite-sample size and power of our test via simulation, obtainingbetter results than other homogeneity test proposed in the literature. Finally, weillustrate the procedure in samples of real heterogeneous data and get consistent results.