{"title":"A note on bias reduction","authors":"C. Withers, S. Nadarajah","doi":"10.5802/CRMATH.49","DOIUrl":null,"url":null,"abstract":"Let ŵ be an unbiased estimate of an unknown w ∈ R. Given a function t (w), we show how to choose a function fn (w) such that for w∗ = ŵ + fn (w), E t ( w∗ )= t (w). We illustrate this with t (w) = w a for a given constant a. For a = 2 and ŵ normal, this leads to the convolution equation cr = cr ⊗ cr . Manuscript received 10th January 2019, accepted 9th April 2020.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":"64 1","pages":"641-644"},"PeriodicalIF":0.8000,"publicationDate":"2020-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comptes Rendus Mathematique","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.5802/CRMATH.49","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let ŵ be an unbiased estimate of an unknown w ∈ R. Given a function t (w), we show how to choose a function fn (w) such that for w∗ = ŵ + fn (w), E t ( w∗ )= t (w). We illustrate this with t (w) = w a for a given constant a. For a = 2 and ŵ normal, this leads to the convolution equation cr = cr ⊗ cr . Manuscript received 10th January 2019, accepted 9th April 2020.
设´´是未知w∈r的无偏估计。给定一个函数t (w),我们展示如何选择一个函数fn (w),使得对于w∗=´´+ fn (w), E t (w∗)= t (w)。对于给定的常数a,我们用t (w) = w a来说明这一点。对于a = 2和´正态,这导致卷积方程cr = cr⊗cr。收稿日期2019年1月10日,收稿日期2020年4月9日。
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