A homogeneity test based on depth-depth plots for functional data
Date:
Abstract: One of the classic concerns in statistics is determining if two samples come from the same population, i.e., homogeneity testing or two-sample testing. In this paper, we propose a homogeneity test in the context of Functional Data Analysis, adopting an idea from multivariate data analysis: the data depth plot (DD-plot). This DD-plot is a generalization of the univariate Q-Q plot (quantile-quantile plot). We propose some statistics based on these DD-plots, and we use bootstrapping techniques to estimate their distributions. We simulate our test’s finite-sample size and power, obtaining better results than other homogeneity tests proposed in the literature. Finally, we illustrate the procedure in samples of real heterogeneous data and get consistent results.