{"paper":{"title":"A Simple Point Estimator of the Power of Moments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andrew Rosalsky, Deli Li, Shuhua Chang, Yongcheng Qi","submitted_at":"2017-03-31T00:03:53Z","abstract_excerpt":"Let $X$ be an observable random variable with unknown distribution function $F(x) = \\mathbb{P}(X \\leq x), - \\infty < x < \\infty$, and let \\[\\ \\theta = \\sup\\left \\{ r \\geq 0:~ \\mathbb{E}|X|^{r} < \\infty \\right \\}. \\] We call $\\theta$ the power of moments of the random variable $X$. Let $X_{1}, X_{2}, ..., X_{n}$ be a random sample of size $n$ drawn from $F(\\cdot)$. In this paper we propose the following simple point estimator of $\\theta$ and investigate its asymptotic properties: \\[ \\hat{\\theta}_{n} = \\frac{\\log n}{\\log \\max_{1 \\leq k \\leq n} |X_{k}|}, \\] where $\\log x = \\ln(e \\vee x), ~- \\inft"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10716","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"}