{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:27JMKLHAXUU2D2YQFXGRJRCGI3","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d0b915030f74c851b35baa0e049ef4e16c1f8c6662b4571ff8a3d9baf3da5285","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-05-18T06:26:26Z","title_canon_sha256":"a9d8981e6cb618854dd5529e4903289b85fdab1a0acc1c3532391df98ba59b97"},"schema_version":"1.0","source":{"id":"1705.06427","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.06427","created_at":"2026-05-18T00:44:14Z"},{"alias_kind":"arxiv_version","alias_value":"1705.06427v1","created_at":"2026-05-18T00:44:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.06427","created_at":"2026-05-18T00:44:14Z"},{"alias_kind":"pith_short_12","alias_value":"27JMKLHAXUU2","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"27JMKLHAXUU2D2YQ","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"27JMKLHA","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:463fe9ff6ec1acdb764c583bc3eb17542bf33fd735fff3f54eee78a4c3914919","target":"graph","created_at":"2026-05-18T00:44:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Spatial-sign covariance matrix (SSCM) is an important substitute of sample covariance matrix (SCM) in robust statistics. This paper investigates the SSCM on its asymptotic spectral behaviors under high-dimensional elliptical populations, where both the dimension $p$ of observations and the sample size $n$ tend to infinity with their ratio $p/n\\to c\\in (0, \\infty)$. The empirical spectral distribution of this nonparametric scatter matrix is shown to converge in distribution to a generalized Mar\\v{c}enko-Pastur law. Beyond this, a new central limit theorem (CLT) for general linear spectral stati","authors_text":"Wang Zhou, Weiming Li","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-05-18T06:26:26Z","title":"On spectral properties of high-dimensional spatial-sign covariance matrices in elliptical distributions with applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06427","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9595cf4b1ff4aea18e3dff5d467243509feceb4587d478ffe3d0281857c1c094","target":"record","created_at":"2026-05-18T00:44:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d0b915030f74c851b35baa0e049ef4e16c1f8c6662b4571ff8a3d9baf3da5285","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-05-18T06:26:26Z","title_canon_sha256":"a9d8981e6cb618854dd5529e4903289b85fdab1a0acc1c3532391df98ba59b97"},"schema_version":"1.0","source":{"id":"1705.06427","kind":"arxiv","version":1}},"canonical_sha256":"d7d2c52ce0bd29a1eb102dcd14c44646d9867ed3bec5d70cd082f9ea84214e50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7d2c52ce0bd29a1eb102dcd14c44646d9867ed3bec5d70cd082f9ea84214e50","first_computed_at":"2026-05-18T00:44:14.795188Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:14.795188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kaFFWpBF3MNMH1SBtOZWvf8HGCZ9t2iH02137dkAbmtNviUNRwLD4e6/+JCKSF9YuuL+8HUA9nit5qEl0km8DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:14.795868Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.06427","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9595cf4b1ff4aea18e3dff5d467243509feceb4587d478ffe3d0281857c1c094","sha256:463fe9ff6ec1acdb764c583bc3eb17542bf33fd735fff3f54eee78a4c3914919"],"state_sha256":"0a5a27074b4fe77a7049e1dbd99566a41beb1395ed731edd3a4fa6026ba230b5"}