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Then, under certain conditions, we consider the estimation of the quadratic functional $\\int_{\\mathbb{R}} f^2(x) \\,dx$ by using the kernel estimator \\[ T_n(h_n)=\\frac{2}{n(n-1)h_n}\\sum_{1\\leq j<i\\leq n}K\\left(\\frac{X_i-X_j}{h_n}\\right). \\] The simulation study for long memory linear processes with symmetric $\\alpha$-stable innovations is also given."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2210.03644","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.ST","submitted_at":"2022-10-07T15:53:28Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"b1a43e11c270cd3d4f440edb560f2b9369642085997cacc91beeb72c031e9de0","abstract_canon_sha256":"a96ec308db0ee5380fa192e6e7aa423198dbb11755fec1bb285affbf43a4b54b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:04:22.337044Z","signature_b64":"eSfhNsG70BxqM0lpc7vdVXCh3H9Ymyl8BOmK52ryEzoDuwoj2ycc1ocmnwwggYJTQ7DBgU3wy+LmuVO80PN+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f415ebde09dec9d16191b9b21e3b124c6a423459ef15a873bb001409977a45a","last_reissued_at":"2026-07-05T05:04:22.336715Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:04:22.336715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Kernel entropy estimation for long memory linear processes with infinite variance","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Fangjun Xu, Hui Liu","submitted_at":"2022-10-07T15:53:28Z","abstract_excerpt":"Let $X=\\{X_n: n\\in\\mathbb{N}\\}$ be a long memory linear process with innovations in the domain of attraction of an $\\alpha$-stable law $(0<\\alpha<2)$. 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