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

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.