高维非正态总体协方差阵检验的检验统计量
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摘要
在大维情形下的统计检验中,一个流行的检验是协方差阵Σ是否为单位阵I,其中重要的环节就是基于tr(Σ-I)~2给出检验统计量。本文的主要内容是给出tr(Σ-I)~2的一个无偏估计量,并利用模拟实验与其他已有的估计量进行比较,也得出了我们给出的估计的优良性。而且运用本文提出的估计量,对收集在校大学生通话数据的总体协方差阵函数进行了估计。
In the statistical test of the large dimensional case,H_0: Σ = I is a popular test. It is important in this test to give the test statistics base to tr( Σ-I)~2. In this article,we propose the unbiased estimate for tr( Σ-I)~2. And through the simulation,we compare with existing estimates. We confirmed the goodness of our proposed estimate.
In the statistical test of the large dimensional case,H_0: Σ = I is a popular test. It is important in this test to give the test statistics base to tr( Σ-I)~2. In this article,we propose the unbiased estimate for tr( Σ-I)~2. And through the simulation,we compare with existing estimates. We confirmed the goodness of our proposed estimate.
引文
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[7]Thomas J Fisher.On testing for an identity covariance matrix when the dimensionality equals or exceeds the sample size[J].Journal of Statistical Planning and Inference,2012(142):312-326.
[8]Tetsuto Himenoa,Takayuki Yamada.Estimations for some functions of covariance matrix in high dimension under non-normality and its applications[J].Journal of Multivariate Analysis,2014(130):27-44.
[9]Cai Tony,Ma Zongming.Optimal hypothesis testing for high dimensional covariance matrices[J].Bernoulli,2013(19):2359-2388.
[10]Chen Songxi,Zhang Lixin,Zhong Pingshou.Testing for high dimensional covariance matrices[J].Journal of the American Statistical Association,2010(105):810-819.
[2]Jiang Tiefeng,Yang Fan.Central limit theorems for classical likelihood ratio tests for high-dimensional normal distributions[J].The Annals of Statistics,2013(41):2029-2074.
[3]Chen Binbin,Pan Guangming.CLT for linear spectral statistics of normalized sample covariance matrices with the dimension much larger than the sample size[J].Bernoulli,2015(21):1089-1133.
[4]Ery Arias-Castro,Sebastien Bubeck,Gabor Lugosi.Detecting positive correlations in a multivariate sample[J].Bernoulli,2015(21):209-241.
[5]Wang Cheng,Yang Jing,Miao Baiqi,et al.Identity tests for high dimensional data using RMT[J].Journal of Multivariate Analysis,2013(118):128-137.
[6]Wang Qinwen,Yao Jianfeng.On the sphericity test with large-dimensional observations[J].Electronic Journal of Statistics,2013(7):2164-2192.
[7]Thomas J Fisher.On testing for an identity covariance matrix when the dimensionality equals or exceeds the sample size[J].Journal of Statistical Planning and Inference,2012(142):312-326.
[8]Tetsuto Himenoa,Takayuki Yamada.Estimations for some functions of covariance matrix in high dimension under non-normality and its applications[J].Journal of Multivariate Analysis,2014(130):27-44.
[9]Cai Tony,Ma Zongming.Optimal hypothesis testing for high dimensional covariance matrices[J].Bernoulli,2013(19):2359-2388.
[10]Chen Songxi,Zhang Lixin,Zhong Pingshou.Testing for high dimensional covariance matrices[J].Journal of the American Statistical Association,2010(105):810-819.