{"paper":{"title":"Tests for the mean of high-dimensional data","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A bootstrap test based on the scaled squared norm of the sample mean yields valid level-alpha inference for high-dimensional means without sparsity or covariance structure assumptions.","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Dietmar Ferger","submitted_at":"2026-05-15T15:08:05Z","abstract_excerpt":"We consider the problem of testing the mean of high-dimensional data when the dimension may grow without explicit rate restrictions relative to the sample size. The proposed procedure is based on the statistic V_n = n||Xn||^2, which avoids inversion of the covariance matrix and is therefore suitable for high-dimensional settings.We establish asymptotic distributional results for both fixed and increasing dimension by embedding the observations into the Hilbert space l2. Furthermore, we prove the asymptotic validity of a bootstrap approximation for the distribution of the test statistic. The re"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The resulting bootstrap test yields asymptotic level-α procedures without requiring sparsity assumptions or structural conditions on the covariance matrix.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The observations can be embedded into the Hilbert space l2 and a new Central Limit Theorem in l2 applies to establish the asymptotic distributional results for both fixed and increasing dimension.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Bootstrap test for high-dimensional mean using squared-norm statistic V_n with asymptotic level-alpha validity via l2 embedding and a new CLT, without sparsity or covariance structure assumptions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A bootstrap test based on the scaled squared norm of the sample mean yields valid level-alpha inference for high-dimensional means without sparsity or covariance structure assumptions.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1ec0c782b0c9116e1d063075c8ea2718dffb14f15b9548d70b503367df705679"},"source":{"id":"2605.16033","kind":"arxiv","version":1},"verdict":{"id":"5031c257-ec06-473c-89cf-248226104278","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T18:44:09.298081Z","strongest_claim":"The resulting bootstrap test yields asymptotic level-α procedures without requiring sparsity assumptions or structural conditions on the covariance matrix.","one_line_summary":"Bootstrap test for high-dimensional mean using squared-norm statistic V_n with asymptotic level-alpha validity via l2 embedding and a new CLT, without sparsity or covariance structure assumptions.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The observations can be embedded into the Hilbert space l2 and a new Central Limit Theorem in l2 applies to establish the asymptotic distributional results for both fixed and increasing dimension.","pith_extraction_headline":"A bootstrap test based on the scaled squared norm of the sample mean yields valid level-alpha inference for high-dimensional means without sparsity or covariance structure assumptions."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16033/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T19:01:18.988255Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T18:51:54.969058Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:41.565117Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T16:41:55.541733Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"fb85530666385b42ad9477c5be68d4fcbf31a50e5a798248c0aaa0da8a40f50f"},"references":{"count":19,"sample":[{"doi":"","year":1980,"title":"A. 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