{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:KS7W3B2EMVFTKXXPSCL6NJLTJF","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":"6b3a4a379b151074111a0452c15b514024d6863032c25b67d1d6a90ba355cf9d","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2009-12-10T15:52:59Z","title_canon_sha256":"cc1ed544474e6a199d518303d6f396b04e9beacf119b3b67fe71a718648cf6e5"},"schema_version":"1.0","source":{"id":"0912.2026","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.2026","created_at":"2026-05-18T04:20:38Z"},{"alias_kind":"arxiv_version","alias_value":"0912.2026v4","created_at":"2026-05-18T04:20:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.2026","created_at":"2026-05-18T04:20:38Z"},{"alias_kind":"pith_short_12","alias_value":"KS7W3B2EMVFT","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"KS7W3B2EMVFTKXXP","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"KS7W3B2E","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:5fb07bbb70336d06e9b2b33cd27339984690f819781448fb80c7938093da8577","target":"graph","created_at":"2026-05-18T04:20:38Z","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":"In this paper, we study the problem of adaptive estimation of the spectral density of a stationary Gaussian process. For this purpose, we consider a wavelet-based method which combines the ideas of wavelet approximation and estimation by information projection in order to warrants that the solution is a nonnegative function. The spectral density of the process is estimated by projecting the wavelet thresholding expansion of the periodogram onto a family of exponential functions. This ensures that the spectral density estimator is a strictly positive function. Then, by Bochner's theorem, the co","authors_text":"Jean-Michel Loubes (IMT), J\\'er\\'emie Bigot (IMT), Lilian Muniz Alvarez, Rolando Biscay Lirio","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2009-12-10T15:52:59Z","title":"Adaptive estimation of spectral densities via wavelet thresholding and information projection"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.2026","kind":"arxiv","version":4},"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":"sha256:83cbe7f8d77dcf55eb602c07f142b15433c54813df3f59aca729cd2368a11355","target":"record","created_at":"2026-05-18T04:20:38Z","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":"6b3a4a379b151074111a0452c15b514024d6863032c25b67d1d6a90ba355cf9d","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2009-12-10T15:52:59Z","title_canon_sha256":"cc1ed544474e6a199d518303d6f396b04e9beacf119b3b67fe71a718648cf6e5"},"schema_version":"1.0","source":{"id":"0912.2026","kind":"arxiv","version":4}},"canonical_sha256":"54bf6d8744654b355eef9097e6a57349458f7ab391a546bcda857027dc980cd5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54bf6d8744654b355eef9097e6a57349458f7ab391a546bcda857027dc980cd5","first_computed_at":"2026-05-18T04:20:38.809228Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:38.809228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sw6NIl3nrx0xCyKUB0k5hDZuA/9ZjlJFlSpsJxQ8zQkL6cJEFCmXON/5jIj8GI9kC6kXzacUiX9Malg3VkAODg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:38.810107Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.2026","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83cbe7f8d77dcf55eb602c07f142b15433c54813df3f59aca729cd2368a11355","sha256:5fb07bbb70336d06e9b2b33cd27339984690f819781448fb80c7938093da8577"],"state_sha256":"4595b9e220e98a7c21c9c1c2dee7f0eb475eff5fe0d668a1366aefdb50b55be4"}