A Two Sample Test based on U-statistic for Functional Data  

作　　者：Wen Juan HU Liang WANG Bao Xue ZHANG Guo Chang WANG 

机构地区：[1]School of Statistics,Capital University of Economics and Business,Beijing 100070,P.R.China [2]School of Mathematics and Statistics,Northeast Normal University,Changchun 130024,P.R.China [3]School of Economics,Jinan University,Guangzhou 510632,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2023年第3期533-552,共20页数学学报（英文版）

基　　金：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)。

摘　　要：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.

关 键 词：Mean test functional data U-STATISTICS two sample 

分 类 号：O212.1[理学—概率论与数理统计]