Bootstrap Methods: Another Look at the Jackknife
Bootstrap Methods: Another Look at the Jackknife
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DOI：
10.1007/978-0-387-75692-9_9
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发表时间：
2008
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影响因子：
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通讯作者：
D. Hinkley
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作者：
D. Hinkley
这是布拉德第一篇关于引导的论文，是他被引用次数最多的作品，目前有2,500次引用。谷歌搜索抛出了超过30万个条目的“埃夫隆，引导。”我认为可以毫不夸张地说，这篇论文开启了统计方法的革命。这场革命的成功很大程度上要归功于布拉德和他周围的人，包括他的几位博士。学生正如布拉德在《埃夫隆》（2003）中所述，他对这个话题的思考始于1972-1973年，当时他和鲁珀特米勒离开宁静的斯坦福大学，去伦敦的帝国学院休假。鲁珀特正在完成他的评论论文（米勒，1974），并就折刀法进行了演讲，这引起了我们许多人的真正兴趣。交叉验证方法也被谈论-默文斯通提出了一份文件（斯通1974年）在这个主题的皇家统计学会在1973年底，但这是集中在choice 1而不是评估，这是布拉德的兴趣。Mosteller和Tukey（1968）在一本关于数据分析的书中提出了折刀法和交叉验证法，同年，布拉德的论文作为Rietz讲座在IMS会议上发表，Mosteller和Tukey（1977）又在第二本书中提出了折刀法和交叉验证法。在20世纪70年代早期到中期，人们对稳健估计产生了相当大的兴趣，部分原因是Peter Huber的理论工作建立在John Tukey的数据分析灵感之上。正如布拉德在1979年的论文中提醒我们的那样，稳健性领域的一个关键产品是Louis Jaeckel在1972年发表的有影响力的手稿，该手稿详细阐述了参数θ的估计T作为统计函数T= t（F）估计θ= t（F）的想法，其中F是经验分布函数。这被用于Jaeckel发展的“无穷小折刀”，包括Fisher delta方法的扩展，通过该方法可以找到T的近似方差，如果T是有限维平均值的可微函数：经验分布函数Δ F只是一个更复杂的平均值。Maurice Quenouille在20世纪50年代开发的原始刀切法是一个非常简单的直接数值计算程序。统计估计偏差的近似值。然后在1958年，John Tukey有趣地提供了用于计算统计估计方差的折刀公式。在一个样本的最简单上下文中，假设估计T= t（X）基于数据向量X=（X1，...，其中Xi是独立随机抽样的结果。写X（− i）for X with
This first paper on the bootstrap is Brad’s most-cited work, currently with some 2,500 citations. A Google search throws up more than 300,000 entries for “Efron, bootstrap.” I think it not an exaggeration to say that the paper started a revolution in statistical methodology. Much of the success of that revolution was due to the rapidity and wide range of consequent developments by Brad and those around him, including several of his Ph. D. students. As Brad has recounted in Efron (2003), his thinking about this topic started in 1972–1973 when he and Rupert Miller left the tranquility of Stanford for sabbatical visits to Imperial College in London. Rupert was finishing his review paper (Miller 1974) and giving talks on jackknife methods, which aroused genuine interest in many of us there. Cross-validation methods were also being talked about–Mervyn Stone presented a paper (Stone 1974) on this topic at the Royal Statistical Society at the end of 1973, but this was focussed on choice1 rather than assessment, which was Brad’s interest. The jackknife and cross-validation methods had both been advocated in a book on data analysis by Mosteller and Tukey (1968), and were again in a second book (Mosteller and Tukey 1977) in the same year that Brad’s paper was presented as the Rietz Lecture at the IMS meeting. Also in the early to mid-1970s there was considerable interest in robust estimation, partly because of Peter Huber’s theoretical work that built on John Tukey’s data analytic inspiration. As Brad reminds us in the 1979 paper, one key product from the robustness area was Louis Jaeckel’s influential 1972 manuscript which elaborated on the idea of an estimate T of a parameter θ as a statistical function T= t (ˆF) estimating θ= t (F), with ˆF the empirical distribution function. This was used in Jaeckel’s development of the “infinitesimal jackknife,” including an extension of the Fisher delta method by which an approximate variance for T could be found if T were a differentiable function of a finite-dimensional average: the empirical distribution function ˆF is just a more complicated average.The original jackknife developed by Maurice Quenouille in the 1950s was a beautifully simple procedure for direct numerical approximation of the bias of a statistical estimate. Then in 1958, John Tukey intriguingly provided the jackknife formula for calculating the variance of a statistical estimate. In the simplest context of one sample, say that the estimate T= t (X) is based on data vector X=(X1,..., Xn) where the Xi’s are outcomes of independent random sampling. Write X (− i) for X with