{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:FIEVJ567SSYAJDCJGXGTA4B6LU","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":"c220fdf9650e6dfeee9bf7f0fd4414759ed01fc7ed25c172bffd4f45866f2f07","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-03-19T06:06:28Z","title_canon_sha256":"80b383b137b3fb85fe597df330ab10857bae146d6b4f649ede4db5d56c1351ee"},"schema_version":"1.0","source":{"id":"1903.07850","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.07850","created_at":"2026-05-17T23:50:53Z"},{"alias_kind":"arxiv_version","alias_value":"1903.07850v1","created_at":"2026-05-17T23:50:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.07850","created_at":"2026-05-17T23:50:53Z"},{"alias_kind":"pith_short_12","alias_value":"FIEVJ567SSYA","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"FIEVJ567SSYAJDCJ","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"FIEVJ567","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:331724cfd90fc5698e753d76db57f28d9537f41137d2a9a3d597b649d2b7916c","target":"graph","created_at":"2026-05-17T23:50:53Z","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 article, we study the performance of the estimator that minimizes $L_{2k}- $ order loss function (for $ k \\ge \\; 2 )$ against the estimators which minimizes the $L_2-$ order loss function (or the least squares estimator). Commonly occurring examples illustrate the differences in efficiency between $L_{2k}$ and $L_2 -$ based estimators. We derive an empirically testable condition under which the $L_{2k}$ estimator is more efficient than the least squares estimator. We construct a simple decision rule to choose between $L_{2k}$ and $L_2$ estimator. Special emphasis is provided to study $","authors_text":"Arijit De, Atanu Biswas, Gopal K Basak, Samarjit Das","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-03-19T06:06:28Z","title":"Relative Efficiency of Higher Normed Estimators Over the Least Squares Estimator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07850","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":"sha256:25e9b5b3130a57ae89e3e1889c6b9c4e2c22769f9f4ebc05bfcad96ebc017485","target":"record","created_at":"2026-05-17T23:50:53Z","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":"c220fdf9650e6dfeee9bf7f0fd4414759ed01fc7ed25c172bffd4f45866f2f07","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-03-19T06:06:28Z","title_canon_sha256":"80b383b137b3fb85fe597df330ab10857bae146d6b4f649ede4db5d56c1351ee"},"schema_version":"1.0","source":{"id":"1903.07850","kind":"arxiv","version":1}},"canonical_sha256":"2a0954f7df94b0048c4935cd30703e5d173632f7abb3b9db3c6c7da41fd74273","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a0954f7df94b0048c4935cd30703e5d173632f7abb3b9db3c6c7da41fd74273","first_computed_at":"2026-05-17T23:50:53.700894Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:53.700894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xU7gKQ6mJIVbDopkYBGgeBtYCaPVrpBksgLnUF/+7ITCqMtuGCJiXUd/f7IvaSA1NDAWX7TmH6goZzKeOYbADw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:53.701646Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.07850","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25e9b5b3130a57ae89e3e1889c6b9c4e2c22769f9f4ebc05bfcad96ebc017485","sha256:331724cfd90fc5698e753d76db57f28d9537f41137d2a9a3d597b649d2b7916c"],"state_sha256":"d68f0e558c2445d902ed09df1b3f08c7bbb5aa89338bb5a64d68acbd63d62bec"}