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5. Detecting Rare andWeak spikes in large covariance matrices

Detecting Rare andWeak spikes in large covariance matrices

来源 :上海交通大学 | 被引量 : 0次 | 上传用户：lequ123123

【摘 要】

：

Given p-dimensional Gaussian vectors Xi iid~N(0,Σ),1≤ i ≤ n,where p ≥ n,we are interested in testing a null hypothesis where Σ = Ip against an alternative hypothesis where all eigenvalues of are 1,e

【作 者】

：

Zheng Tracy Ke 

【机 构】

：

University of Chicago,IL 60637,USA

【出 处】

：

上海交通大学

【发表日期】

：

2016年4期

【关键词】

：

Cumulative sum Higher Criticism Marchenko-Pastur law phase transition Rare and W 

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　　Given p-dimensional Gaussian vectors Xi iid~N(0,Σ),1≤ i ≤ n,where p ≥ n,we are interested in testing a null hypothesis where Σ = Ip against an alternative hypothesis where all eigenvalues of are 1,except for r of them are larger than 1(i.e.,spiked eigenvalues).

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