{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OU576KTVCA42RU66MJOSDEZSUW","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":"21b9ddfbb9ec661bcdc2b89b9a5fae11188291334265de7c44e2a3d15a31cb6a","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-11-27T15:13:49Z","title_canon_sha256":"f05a551525c4e4427a97afbf3566f7a28ad042d407c3f707938ec398b6199b5f"},"schema_version":"1.0","source":{"id":"1511.08698","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.08698","created_at":"2026-05-18T01:01:52Z"},{"alias_kind":"arxiv_version","alias_value":"1511.08698v2","created_at":"2026-05-18T01:01:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08698","created_at":"2026-05-18T01:01:52Z"},{"alias_kind":"pith_short_12","alias_value":"OU576KTVCA42","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OU576KTVCA42RU66","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OU576KTV","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:ee53d68003d5eed9427b044ca16c18a7c6e74403fb5b1e966a71551b92403e35","target":"graph","created_at":"2026-05-18T01:01:52Z","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":"Consider the standard nonparametric regression model and take as estimator the penalized least squares function. In this article, we study the trade-off between closeness to the true function and complexity penalization of the estimator, where complexity is described by a seminorm on a class of functions. First, we present an exponential concentration inequality revealing the concentration behavior of the trade-off of the penalized least squares estimator around a nonrandom quantity, where such quantity depends on the problem under consideration. Then, under some conditions and for the proper ","authors_text":"Alan Muro, Sara van de Geer","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-11-27T15:13:49Z","title":"Concentration behavior of the penalized least squares estimator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08698","kind":"arxiv","version":2},"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:c7b59e818b929437bace4944291a0eb314c67282482ecff6510ad0a5f3691da2","target":"record","created_at":"2026-05-18T01:01:52Z","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":"21b9ddfbb9ec661bcdc2b89b9a5fae11188291334265de7c44e2a3d15a31cb6a","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-11-27T15:13:49Z","title_canon_sha256":"f05a551525c4e4427a97afbf3566f7a28ad042d407c3f707938ec398b6199b5f"},"schema_version":"1.0","source":{"id":"1511.08698","kind":"arxiv","version":2}},"canonical_sha256":"753bff2a751039a8d3de625d219332a597e0b289be505fdbc3dc0ff170c9c5ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"753bff2a751039a8d3de625d219332a597e0b289be505fdbc3dc0ff170c9c5ba","first_computed_at":"2026-05-18T01:01:52.081647Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:52.081647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h6xBRuA4ZOqr1xDHF5P0KN7NdwTdbGjTZi4bDbuxWvjkc7+1Fcdz0MyOE0hzxnGC7bTip7EXr8w2issnK6LcDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:52.082247Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.08698","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7b59e818b929437bace4944291a0eb314c67282482ecff6510ad0a5f3691da2","sha256:ee53d68003d5eed9427b044ca16c18a7c6e74403fb5b1e966a71551b92403e35"],"state_sha256":"5ad8bf5624a058d6400f2ba04c2c0a45ec165596437d9064bad15ddabfff950c"}