{"paper":{"title":"A simple note on some empirical stochastic process as a tool in uniform L-statistics weak laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Gane Samb Lo","submitted_at":"2014-05-22T00:04:40Z","abstract_excerpt":"In this paper, we are concerned with the stochastic process \\begin{equation} \\beta_{n}(q_{t},t)=\\beta_{n}(t)=\\frac{1}{\\sqrt{n}}\\sum_{j=1}^{n}\\left\\{G_{t,n}(Y(t))-G_{t}(Y_{j}(t))\\right\\} q_{t}(Y_{j}(t)), \\tag{A} \\end{equation} where for $n\\geq1$ and $T>0$, the sequences $\\{Y_{1}(t),Y_{2}(t),...,Y_{n}(t),t\\in [0,T]\\}$ are independant observations of some real stochastic process ${Y(t),t\\in [0,T]}$, for each $t \\in [0,T]$, $G_{t}$ is the distribution function of $% Y(t)$ and $G_{t,n}$ is the empirical distribution function based on $% Y_{1}(t),Y_{2}(t),...,Y_{n}(t)$, and finally $q_{t}$ is a boun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5577","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"}