Abstract
We propose a two-sample test for the mean functions of functional data when the number of bases is much lager than the sample size. The novel test is based on U-statistics which avoids estimating the covariance operator accurately under the high dimensional situation. We further prove the asymptotic normality of our test statistic under both null hypothesis and a local alternative hypothesis. An extensive simulation study is presented which shows that the proposed test works well in comparison with several other methods under the high dimensional situation. An application to egg-laying trajectories of Mediterranean fruit flies data set demonstrates the applicability of the method.
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We thank the editors and the reviewers for their time and comments.
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Supported by the National Natural Science Foundation of China (Grant Nos. 11671268 and 12271370), the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2020A1515010821), the Fundamental Research Funds for the Central Universities (Grant No. 12619624), Supported by the Research Start-up Fund for new young Teachers of Capital University of Economics and Business (Grant No. 00592254417068)
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Hu, W.J., Wang, L., Zhang, B.X. et al. A Two Sample Test based on U-statistic for Functional Data. Acta. Math. Sin.-English Ser. 39, 533–552 (2023). https://doi.org/10.1007/s10114-023-1608-x
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DOI: https://doi.org/10.1007/s10114-023-1608-x