{"title":"The History of Bootstrapping: Tracing the Development of Resampling with Replacement","authors":"Denise LaFontaine","doi":"10.54870/1551-3440.1515","DOIUrl":null,"url":null,"abstract":"Sampling is one of the most fundamental concepts in statistics, as the quality and accuracy of the statistical inferences made, heavily depend on the method used to obtain the sample and the sample’s ability to represent the population of inference. Despite being a simple concept, sampling presents researchers with many challenges. Generally, due to monetary and time constraints, researchers must take a smaller sample size than they would ideally use. Using statistics from these small samples, estimates for population parameters can be made, typically in the form of a confidence interval. However, the validity of these confidence intervals depends on three basic assumptions that are difficult to meet with small sample sizes. This paper traces the development of the sampling method known as bootstrapping that helps small samples to meet these assumptions. The paper touches on previous methods used before the development of bootstrapping and shows how bootstrapping has evolved over the last four decades and become widely used in the field of statistics.","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics Enthusiast","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.54870/1551-3440.1515","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 5
Abstract
Sampling is one of the most fundamental concepts in statistics, as the quality and accuracy of the statistical inferences made, heavily depend on the method used to obtain the sample and the sample’s ability to represent the population of inference. Despite being a simple concept, sampling presents researchers with many challenges. Generally, due to monetary and time constraints, researchers must take a smaller sample size than they would ideally use. Using statistics from these small samples, estimates for population parameters can be made, typically in the form of a confidence interval. However, the validity of these confidence intervals depends on three basic assumptions that are difficult to meet with small sample sizes. This paper traces the development of the sampling method known as bootstrapping that helps small samples to meet these assumptions. The paper touches on previous methods used before the development of bootstrapping and shows how bootstrapping has evolved over the last four decades and become widely used in the field of statistics.
期刊介绍:
The Mathematics Enthusiast (TME) is an eclectic internationally circulated peer reviewed journal which focuses on mathematics content, mathematics education research, innovation, interdisciplinary issues and pedagogy. The journal exists as an independent entity. The electronic version is hosted by the Department of Mathematical Sciences- University of Montana. The journal is NOT affiliated to nor subsidized by any professional organizations but supports PMENA [Psychology of Mathematics Education- North America] through special issues on various research topics. TME strives to promote equity internationally by adopting an open access policy, as well as allowing authors to retain full copyright of their scholarship contingent on the journals’ publication ethics guidelines. Authors do not need to be affiliated with the University of Montana in order to publish in this journal. Journal articles cover a wide spectrum of topics such as mathematics content (including advanced mathematics), educational studies related to mathematics, and reports of innovative pedagogical practices with the hope of stimulating dialogue between pre-service and practicing teachers, university educators and mathematicians. The journal is interested in research based articles as well as historical, philosophical, political, cross-cultural and systems perspectives on mathematics content, its teaching and learning. The journal also includes a monograph series on special topics of interest to the community of readers.