{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:BAJQP4GCB7ISAR22XHEIY73XFD","short_pith_number":"pith:BAJQP4GC","canonical_record":{"source":{"id":"1610.09139","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-10-28T09:25:28Z","cross_cats_sorted":[],"title_canon_sha256":"c58eb7b87d6b67ba4a86f52bf4f24b9f0d81a1131810a72194529da0605e287b","abstract_canon_sha256":"de9687f2e499a56afb8ade1769507abb86f341af573f40b18c2c6fe7cba5f4e4"},"schema_version":"1.0"},"canonical_sha256":"081307f0c20fd120475ab9c88c7f7728e6189444f0932ce0ccef60e8cd4da2ae","source":{"kind":"arxiv","id":"1610.09139","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09139","created_at":"2026-05-18T00:23:01Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09139v3","created_at":"2026-05-18T00:23:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09139","created_at":"2026-05-18T00:23:01Z"},{"alias_kind":"pith_short_12","alias_value":"BAJQP4GCB7IS","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BAJQP4GCB7ISAR22","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BAJQP4GC","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:BAJQP4GCB7ISAR22XHEIY73XFD","target":"record","payload":{"canonical_record":{"source":{"id":"1610.09139","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-10-28T09:25:28Z","cross_cats_sorted":[],"title_canon_sha256":"c58eb7b87d6b67ba4a86f52bf4f24b9f0d81a1131810a72194529da0605e287b","abstract_canon_sha256":"de9687f2e499a56afb8ade1769507abb86f341af573f40b18c2c6fe7cba5f4e4"},"schema_version":"1.0"},"canonical_sha256":"081307f0c20fd120475ab9c88c7f7728e6189444f0932ce0ccef60e8cd4da2ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:01.552494Z","signature_b64":"bVudB69H9Xh0kSPiqTVtQZukPyvmKzZYKxivOvrXUBHxyhEvGvUI1vZe5kyKIRImLf4XnaXpjeNfJVOt80GsCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"081307f0c20fd120475ab9c88c7f7728e6189444f0932ce0ccef60e8cd4da2ae","last_reissued_at":"2026-05-18T00:23:01.551822Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:01.551822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.09139","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:23:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gv4L1Zdfsiy8oUISOqmn1jfGw24rK+ExcHLsSwOIqW2LSSa+FB0LHkqgppOQcfT2dmrHZGoGKnJMzceS6Zf9Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:46:59.317831Z"},"content_sha256":"5b34b4acf0cc819469afaacff4a44476aebf7ddad8dd60d53e85ad92643d528e","schema_version":"1.0","event_id":"sha256:5b34b4acf0cc819469afaacff4a44476aebf7ddad8dd60d53e85ad92643d528e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:BAJQP4GCB7ISAR22XHEIY73XFD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Detecting heteroskedasticity in nonparametric regression using weighted empirical processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Justin Chown, Ursula U. M\\\"uller","submitted_at":"2016-10-28T09:25:28Z","abstract_excerpt":"Heteroskedastic errors can lead to inaccurate statistical conclusions if they are not properly handled. We introduce a test for heteroskedasticity for the nonparametric regression model with multiple covariates. It is based on a suitable residual-based empirical distribution function. The residuals are constructed using local polynomial smoothing. Our test statistic involves a detection function that can verify heteroskedasticity by exploiting just the independence-dependence structure between the detection function and model errors, i.e. we do not require a specific model of the variance func"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09139","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:23:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YihZAszTDUx9CKfrGQ1g2PKoNb6YK3gwPOqPcrClJTcHBb+D+o8oxHs8xXthdpbtcY3+4Pg/l7cSqrWmpTkIDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:46:59.318180Z"},"content_sha256":"30ef040ca2a8c8da669f9e863cfa3574ad8f1c0ee4bc27844381b5c48aa72308","schema_version":"1.0","event_id":"sha256:30ef040ca2a8c8da669f9e863cfa3574ad8f1c0ee4bc27844381b5c48aa72308"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BAJQP4GCB7ISAR22XHEIY73XFD/bundle.json","state_url":"https://pith.science/pith/BAJQP4GCB7ISAR22XHEIY73XFD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BAJQP4GCB7ISAR22XHEIY73XFD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T20:46:59Z","links":{"resolver":"https://pith.science/pith/BAJQP4GCB7ISAR22XHEIY73XFD","bundle":"https://pith.science/pith/BAJQP4GCB7ISAR22XHEIY73XFD/bundle.json","state":"https://pith.science/pith/BAJQP4GCB7ISAR22XHEIY73XFD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BAJQP4GCB7ISAR22XHEIY73XFD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BAJQP4GCB7ISAR22XHEIY73XFD","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":"de9687f2e499a56afb8ade1769507abb86f341af573f40b18c2c6fe7cba5f4e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-10-28T09:25:28Z","title_canon_sha256":"c58eb7b87d6b67ba4a86f52bf4f24b9f0d81a1131810a72194529da0605e287b"},"schema_version":"1.0","source":{"id":"1610.09139","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09139","created_at":"2026-05-18T00:23:01Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09139v3","created_at":"2026-05-18T00:23:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09139","created_at":"2026-05-18T00:23:01Z"},{"alias_kind":"pith_short_12","alias_value":"BAJQP4GCB7IS","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BAJQP4GCB7ISAR22","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BAJQP4GC","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:30ef040ca2a8c8da669f9e863cfa3574ad8f1c0ee4bc27844381b5c48aa72308","target":"graph","created_at":"2026-05-18T00:23:01Z","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":"Heteroskedastic errors can lead to inaccurate statistical conclusions if they are not properly handled. We introduce a test for heteroskedasticity for the nonparametric regression model with multiple covariates. It is based on a suitable residual-based empirical distribution function. The residuals are constructed using local polynomial smoothing. Our test statistic involves a detection function that can verify heteroskedasticity by exploiting just the independence-dependence structure between the detection function and model errors, i.e. we do not require a specific model of the variance func","authors_text":"Justin Chown, Ursula U. M\\\"uller","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-10-28T09:25:28Z","title":"Detecting heteroskedasticity in nonparametric regression using weighted empirical processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09139","kind":"arxiv","version":3},"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":"sha256:5b34b4acf0cc819469afaacff4a44476aebf7ddad8dd60d53e85ad92643d528e","target":"record","created_at":"2026-05-18T00:23:01Z","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":"de9687f2e499a56afb8ade1769507abb86f341af573f40b18c2c6fe7cba5f4e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-10-28T09:25:28Z","title_canon_sha256":"c58eb7b87d6b67ba4a86f52bf4f24b9f0d81a1131810a72194529da0605e287b"},"schema_version":"1.0","source":{"id":"1610.09139","kind":"arxiv","version":3}},"canonical_sha256":"081307f0c20fd120475ab9c88c7f7728e6189444f0932ce0ccef60e8cd4da2ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"081307f0c20fd120475ab9c88c7f7728e6189444f0932ce0ccef60e8cd4da2ae","first_computed_at":"2026-05-18T00:23:01.551822Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:01.551822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bVudB69H9Xh0kSPiqTVtQZukPyvmKzZYKxivOvrXUBHxyhEvGvUI1vZe5kyKIRImLf4XnaXpjeNfJVOt80GsCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:01.552494Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.09139","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b34b4acf0cc819469afaacff4a44476aebf7ddad8dd60d53e85ad92643d528e","sha256:30ef040ca2a8c8da669f9e863cfa3574ad8f1c0ee4bc27844381b5c48aa72308"],"state_sha256":"d7adde1e86d1f22aa74da1850c056b03f46ee90c8cea9b23634b919bc5f96bb6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tf1AHjQL9T8o40Cz6iILmu4i934wSGiqYodBevUAvBdcFmfNaWoR1i/kuqRLmCFB01/8CCtinoR+RXtYaA9YCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T20:46:59.320222Z","bundle_sha256":"7ec7420aba52cdb119accb4fbd2f1908705633f5b3f7a06350ac590550ded53c"}}