The History of Bootstrapping: Tracing the Development of Resampling with Replacement

IF 0.3 Q4 MATHEMATICS
Denise LaFontaine
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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.
自举的历史:追溯带替换的重采样的发展
抽样是统计学中最基本的概念之一,因为统计推断的质量和准确性在很大程度上取决于获取样本的方法以及样本代表推断总体的能力。尽管抽样是一个简单的概念,但它给研究人员带来了许多挑战。通常,由于资金和时间的限制,研究人员必须采用比理想情况下更小的样本量。利用这些小样本的统计数据,可以对总体参数进行估计,通常以置信区间的形式。然而,这些置信区间的有效性取决于三个基本假设,这些假设很难满足小样本量。本文追溯了被称为自举的抽样方法的发展,该方法可以帮助小样本满足这些假设。本文触及以前使用的方法之前的自举发展,并显示如何自举已演变在过去的四十年,并成为广泛应用于统计领域。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Mathematics Enthusiast
Mathematics Enthusiast MATHEMATICS-
CiteScore
1.40
自引率
0.00%
发文量
43
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.
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