高频函数型数据均值的随机化检验  

Randomized Test of Mean Function for High-frequency Functional Data

作　　者：赵繁荣 岳莉莉 张宝学 ZHAO FANRONG;YUE LILI;ZHANG BAOXUE(School of Mathematical Sciences,Shanri University,Taiyuan 030006,China;School of Statistics and Data Science,Nanjing Audit University,Nanjing 211815,China;School of Statistics,Capital University of Economics and Business,Beijing 100071,China)

机构地区：[1]山西大学数学科学学院,太原030006 [2]南京审计大学统计与数据科学学院,南京211815 [3]首都经济贸易大学统计学院,北京100071

出　　处：《应用数学学报》2024年第2期238-254,共17页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(批准号:12301349,12271370,12001277);山西省自然科学基金(批准号:202203021222009)资助项目。

摘　　要：本文研究高频函数型数据均值的检验问题.对选取主成分个数无限且协方差算子具有离群特征根的函数型数据,由于样本量的不足和协方差算子的强条件,经典的基于函数主成分降维方法构造的卡方或混合卡方检验会失效.因此针对该问题本文提出一种随机化检验,并证明其大样本性质,进一步用有限样本的数值模拟研究来验证该方法的有效性,最后将该方法应用到基准音素数据中.This paper studies the problem of testing the mean of high-frequency func-tional data.For functional data with infinite number of principal components and spiked eigenvalues of covariance operators,the classical Chi-square or mixed Chi-square test constructed based on the dimension reduction method using functional principal components will become invalid due to insufficient sample size and strong conditions of covariance operators.Therefore,this paper proposes a randomized test to solve this problem,and proves the large sample properties.Further,the numerical simulation of limited samples is used to verify the effectiveness of the proposed test.Finally,this method is applied to the phoneme data.

关 键 词：高频函数型数据 均值函数 随机化检验 渐近性质 

分 类 号：O212.1[理学—概率论与数理统计]