{"paper":{"title":"Sharp minimax tests for large Toeplitz covariance matrices with repeated observations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Cristina Butucea, Rania Zgheib","submitted_at":"2015-06-04T12:04:59Z","abstract_excerpt":"We observe a sample of $n$ independent $p$-dimensional Gaussian vectors with Toeplitz covariance matrix $ \\Sigma = [\\sigma_{|i-j|}]_{1 \\leq i,j \\leq p}$ and $\\sigma_0=1$. We consider the problem of testing the hypothesis that $\\Sigma$ is the identity matrix asymptotically when $n \\to \\infty$ and $p \\to \\infty$. We suppose that the covariances $\\sigma_k$ decrease either polynomially ($\\sum_{k \\geq 1} k^{2\\alpha} \\sigma^2_{k} \\leq L$ for $ \\alpha >1/4$ and $L>0$) or exponentially ($\\sum_{k \\geq 1} e^{2Ak} \\sigma^2_{k} \\leq L$ for $ A,L>0$).\n  We consider a test procedure based on a weighted U-st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01557","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}