125 citations
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math.ST2015★ 1 cited
Sharp minimax tests for large Toeplitz covariance matrices with repeated observations
Cristina Butucea, Rania Zgheib
We observe a sample of independent -dimensional Gaussian vectors with Toeplitz covariance matrix and . We consider the problem o…
math.ST2015★ 66 cited
Minimax estimation of linear and quadratic functionals on sparsity classes
Olivier Collier, Laëtitia Comminges, Alexandre B. Tsybakov
For the Gaussian sequence model, we obtain non-asymptotic minimax rates of estimation of the linear, quadratic and the L2-norm functionals on classes of sparse vectors and construc…