{"paper":{"title":"The strong representation for the nonparametric estimation of length-biased and right-censored data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Jianhua Shi, Xiaoping Chen, Yong Zhou","submitted_at":"2014-09-16T13:53:13Z","abstract_excerpt":"In this article, we consider a useful product-limit estimator of distribution function proposed by Huang & Qin(2011) when the observations are subject to length-biased and right-censored data. The estimator retains the simple closed-form expression of the truncation product-limit estimator with some good properties. An almost sure representation for the estimator is obtained which can be used to derive many properties of functional statistics based on this product-limit estimator. The rate for the remainder in the representation is of order $O(n^{-3/4}(\\log(n)^{3/4}) $ a.s."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4642","kind":"arxiv","version":2},"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"}