Sharp minimax tests for large Toeplitz covariance matrices with repeated observations

Cristina Butucea, Rania Zgheib

We observe a sample of $n$ independent $p$-dimensional Gaussian vectors with Toeplitz covariance matrix $\Sigma =[{\sigma }_{|i-j|}{]}_{1\le i,j\le p}$ and ${\sigma }_0=1$. We consider the problem o…