Sharp minimax tests for large Toeplitz covariance matrices with repeated observations

Cristina Butucea and Rania Zgheib

Journal of Multivariate Analysis, 2016, vol. 146, issue C, 164-176

Abstract: We observe a sample of n independent p-dimensional Gaussian vectors with Toeplitz covariance matrix Σ=[σ∣i−j∣]1≤i,j≤p and σ0=1. We consider the problem of testing the hypothesis that Σ is the identity matrix asymptotically when n→∞ and p→∞. We suppose that the covariances σk decrease either polynomially (∑k≥1k2ασk2≤L for α>1/4 and L>0) or exponentially (∑k≥1e2Akσk2≤L for A,L>0).

Keywords: Toeplitz matrix; Covariance matrix; High-dimensional data; U-statistic; Minimax hypothesis testing; Optimal separation rates; Sharp asymptotic rates (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.jmva.2015.09.003

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