{"title":"Simpler bootstrap estimation of the asymptotic variance of U-statistic-based estimators","authors":"Bo E. Honoré, Luojia Hu","doi":"10.1111/ectj.12099","DOIUrl":null,"url":null,"abstract":"The bootstrap is a popular and useful tool for estimating the asymptotic variance of complicated estimators. Ironically, the fact that the estimators are complicated can make the standard bootstrap computationally burdensome because it requires repeated re-calculation of the estimator. In Honore and Hu (2015), we propose a computationally simpler bootstrap procedure based on repeated re-calculation of one-dimensional estimators. The applicability of that approach is quite general. In this paper, we propose an alternative method which is specific to extremum estimators based on U-statistics. The contribution here is that rather than repeated re-calculating the U-statistic-based estimator, we can recalculate a related estimator based on single-sums. A simulation study suggests that the approach leads to a good approximation to the standard bootstrap, and that if this is the goal, then our approach is superior to numerical derivative methods.","PeriodicalId":50555,"journal":{"name":"Econometrics Journal","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2017-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/ectj.12099","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Econometrics Journal","FirstCategoryId":"96","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/ectj.12099","RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ECONOMICS","Score":null,"Total":0}
引用次数: 3
Abstract
The bootstrap is a popular and useful tool for estimating the asymptotic variance of complicated estimators. Ironically, the fact that the estimators are complicated can make the standard bootstrap computationally burdensome because it requires repeated re-calculation of the estimator. In Honore and Hu (2015), we propose a computationally simpler bootstrap procedure based on repeated re-calculation of one-dimensional estimators. The applicability of that approach is quite general. In this paper, we propose an alternative method which is specific to extremum estimators based on U-statistics. The contribution here is that rather than repeated re-calculating the U-statistic-based estimator, we can recalculate a related estimator based on single-sums. A simulation study suggests that the approach leads to a good approximation to the standard bootstrap, and that if this is the goal, then our approach is superior to numerical derivative methods.
期刊介绍:
The Econometrics Journal was established in 1998 by the Royal Economic Society with the aim of creating a top international field journal for the publication of econometric research with a standard of intellectual rigour and academic standing similar to those of the pre-existing top field journals in econometrics. The Econometrics Journal is committed to publishing first-class papers in macro-, micro- and financial econometrics. It is a general journal for econometric research open to all areas of econometrics, whether applied, computational, methodological or theoretical contributions.