Abstract
In this paper, we consider the two-sample problem for univariate and multivariate functional data. To solve this problem, we use tool of characteristic function and a basis function representation of functional data. We construct test statistics for conformity of distributions based on a weighted distance between characteristic functions of random vectors obtained in basis representation. Different weight functions result in different test statistics, whose distributions are approximated by permutation method. Testing procedures are implemented in the R program and the code is available. Simulation study shows good finite sample properties of proposed methods, while real data example illustrates the application of them.
Highlights
Over the last three decades, real-time measurement instruments and data storage computer resources have significantly developed
We have proposed the new permutation tests for the two-sample problem for functional data
Using characteristic function representation of this two-sample problem and basis function representation of functional data, we have reduced this problem to the multivariate two-sample problem
Summary
Over the last three decades, real-time measurement instruments and data storage computer resources have significantly developed. The two-sample test for conformity of distributions is one of the statistical methods that have been generalized for functional data It is rarely considered in the literature, and it is not so popular as the analysis of variance problem for functional data (see, for example, Gorecki and Smaga 2017, 2019; Zhang 2013). The present paper considers methods based on characteristic functions of random processes and their basis function representation. Chen, Meintanis, and Zhu (2019) investigated this problem and proposed to use a density of some random distribution as the weight function Their method has similar theoretical properties to the energy statistic. The supplementary materials to this paper contain the code of R programming language (R Core Team 2019) for numerical experiments
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