{"paper":{"title":"Kernel entropy estimation for linear processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Fangjun Xu, Hailing Sang, Yongli Sang","submitted_at":"2017-12-01T05:07:13Z","abstract_excerpt":"Let $\\{X_n: n\\in \\mathbb{N}\\}$ be a linear process with bounded probability density function $f(x)$. We study the estimation of the quadratic functional $\\int_{\\mathbb{R}} f^2(x)\\, dx$. With a Fourier transform on the kernel function and the projection method, it is shown that, under certain mild conditions, the estimator \\[ \\frac{2}{n(n-1)h_n} \\sum_{1\\le i<j\\le n}K\\left(\\frac{X_i-X_j}{h_n}\\right) \\] has similar asymptotical properties as the i.i.d. case studied in Gin\\'{e} and Nickl (2008) if the linear process $\\{X_n: n\\in \\mathbb{N}\\}$ has the defined short range dependence. We also provide"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00196","kind":"arxiv","version":1},"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"}