{"paper":{"title":"Marked empirical processes for non-stationary time series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Ngai Hang Chan, Rongmao Zhang","submitted_at":"2013-12-11T11:26:14Z","abstract_excerpt":"Consider a first-order autoregressive process $X_i=\\beta X_{i-1}+\\varepsilon_i,$ where $\\varepsilon_i=G(\\eta_i,\\eta_{i-1},\\ldots)$ and $\\eta_i,i\\in\\mathbb{Z}$ are i.i.d. random variables. Motivated by two important issues for the inference of this model, namely, the quantile inference for $H_0: \\beta=1$, and the goodness-of-fit for the unit root model, the notion of the marked empirical process $\\alpha_n(x)=\\frac{1}{n}\\sum_{i=1}^ng(X_i/a_n)I(\\varepsilon_i\\leq x),x\\in\\mathbb{R}$ is investigated in this paper. Herein, $g(\\cdot)$ is a continuous function on $\\mathbb{R}$ and $\\{a_n\\}$ is a sequenc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3120","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"}