{"title":"同时计算 Kendall's tau 及其 jackknife 方差","authors":"Samuel Perreault","doi":"10.1016/j.spl.2024.110181","DOIUrl":null,"url":null,"abstract":"<div><p>We present efficient algorithms for simultaneously computing Kendall’s tau and the jackknife estimator of its variance. For the classical pairwise tau, we describe a modification of Knight’s algorithm (originally designed to compute only tau) that does so while preserving its <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>n</mi><msub><mrow><mo>log</mo></mrow><mrow><mn>2</mn></mrow></msub><mi>n</mi><mo>)</mo></mrow></mrow></math></span> runtime in the number of observations <span><math><mi>n</mi></math></span>. We also introduce a novel algorithm computing a multivariate extension of tau and its jackknife variance in <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>n</mi><msubsup><mrow><mo>log</mo></mrow><mrow><mn>2</mn></mrow><mrow><mi>p</mi></mrow></msubsup><mi>n</mi><mo>)</mo></mrow></mrow></math></span> time.</p></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"213 ","pages":"Article 110181"},"PeriodicalIF":0.9000,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167715224001500/pdfft?md5=5b3841ee52600a218d235751bb715c3c&pid=1-s2.0-S0167715224001500-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Simultaneous computation of Kendall’s tau and its jackknife variance\",\"authors\":\"Samuel Perreault\",\"doi\":\"10.1016/j.spl.2024.110181\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We present efficient algorithms for simultaneously computing Kendall’s tau and the jackknife estimator of its variance. For the classical pairwise tau, we describe a modification of Knight’s algorithm (originally designed to compute only tau) that does so while preserving its <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>n</mi><msub><mrow><mo>log</mo></mrow><mrow><mn>2</mn></mrow></msub><mi>n</mi><mo>)</mo></mrow></mrow></math></span> runtime in the number of observations <span><math><mi>n</mi></math></span>. We also introduce a novel algorithm computing a multivariate extension of tau and its jackknife variance in <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>n</mi><msubsup><mrow><mo>log</mo></mrow><mrow><mn>2</mn></mrow><mrow><mi>p</mi></mrow></msubsup><mi>n</mi><mo>)</mo></mrow></mrow></math></span> time.</p></div>\",\"PeriodicalId\":49475,\"journal\":{\"name\":\"Statistics & Probability Letters\",\"volume\":\"213 \",\"pages\":\"Article 110181\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-06-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0167715224001500/pdfft?md5=5b3841ee52600a218d235751bb715c3c&pid=1-s2.0-S0167715224001500-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Statistics & Probability Letters\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0167715224001500\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistics & Probability Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167715224001500","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
摘要
我们提出了同时计算 Kendall's tau 及其方差的 jackknife 估计数的高效算法。对于经典的成对 tau,我们描述了对 Knight 算法(最初只设计用于计算 tau)的一种修改,该算法在计算 tau 的同时,还能保持其在观测值 n 数量下的 O(nlog2n) 运行时间。我们还介绍了一种新算法,该算法能在 O(nlog2pn) 时间内计算 tau 的多变量扩展及其 jackknife 方差。
Simultaneous computation of Kendall’s tau and its jackknife variance
We present efficient algorithms for simultaneously computing Kendall’s tau and the jackknife estimator of its variance. For the classical pairwise tau, we describe a modification of Knight’s algorithm (originally designed to compute only tau) that does so while preserving its runtime in the number of observations . We also introduce a novel algorithm computing a multivariate extension of tau and its jackknife variance in time.
期刊介绍:
Statistics & Probability Letters adopts a novel and highly innovative approach to the publication of research findings in statistics and probability. It features concise articles, rapid publication and broad coverage of the statistics and probability literature.
Statistics & Probability Letters is a refereed journal. Articles will be limited to six journal pages (13 double-space typed pages) including references and figures. Apart from the six-page limitation, originality, quality and clarity will be the criteria for choosing the material to be published in Statistics & Probability Letters. Every attempt will be made to provide the first review of a submitted manuscript within three months of submission.
The proliferation of literature and long publication delays have made it difficult for researchers and practitioners to keep up with new developments outside of, or even within, their specialization. The aim of Statistics & Probability Letters is to help to alleviate this problem. Concise communications (letters) allow readers to quickly and easily digest large amounts of material and to stay up-to-date with developments in all areas of statistics and probability.
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