Distribution/correlation-free test for two-sample means in high-dimensional functional data with eigenvalue decay relaxed

作     者：Kaijie Xue 

作者机构：School of Statistics and Data ScienceNankai UniversityTianjin 300071China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2023年第66卷第10期

页      面：2337-2346页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China (Grant No.11901313) Fundamental Research Funds for the Central Universities Key Laboratory for Medical Data Analysis and Statistical Research of Tianjin Key Laboratory of Pure Mathematics and Combinatorics 

主　　题：high dimension functional data eigenvalue decay relaxed multiplier bootstrap distribution/correlation-free 

摘      要：We propose a methodology for testing two-sample means in high-dimensional functional data that requires no decaying pattern on eigenvalues of the functional *** the best of our knowledge,we are the first to consider and address such a *** be specific,we devise a confidence region for the mean curve difference between two samples,which directly establishes a rigorous inferential procedure based on the multiplier *** addition,the proposed test permits the functional observations in each sample to have mutually different distributions and arbitrary correlation structures,which is regarded as the desired property of distribution/correlation-free,leading to a more challenging scenario for theoretical *** desired properties include the allowance for highly unequal sample sizes,exponentially growing data dimension in sample sizes and consistent power behavior under fairly general *** proposed test is shown uniformly convergent to the prescribed significance,and its finite sample performance is evaluated via the simulation study and an application to electroencephalography data.