{"title":"Looking back: Selected contributions by C. R. Rao to multivariate analysis","authors":"Dianna Smith","doi":"10.1111/sjos.12749","DOIUrl":null,"url":null,"abstract":"Statistician C. R. Rao made many contributions to multivariate analysis over the span of his career. Some of his earliest contributions continue to be used and built upon almost 80 years later, while his more recent contributions spur new avenues of research. The present article discusses these contributions, how they helped shape multivariate analysis as we see it today, and what we may learn from reviewing his works. Topics include his extension of linear discriminant analysis, Rao's perimeter test, Rao's U statistic, his asymptotic expansion of Wilks' statistic, canonical factor analysis, functional principal component analysis, redundancy analysis, canonical coordinates, and correspondence analysis. The examination of his works shows that interdisciplinary collaboration and the utilization of real datasets were crucial in almost all of Rao's impactful contributions.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Scandinavian Journal of Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1111/sjos.12749","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
Abstract
Statistician C. R. Rao made many contributions to multivariate analysis over the span of his career. Some of his earliest contributions continue to be used and built upon almost 80 years later, while his more recent contributions spur new avenues of research. The present article discusses these contributions, how they helped shape multivariate analysis as we see it today, and what we may learn from reviewing his works. Topics include his extension of linear discriminant analysis, Rao's perimeter test, Rao's U statistic, his asymptotic expansion of Wilks' statistic, canonical factor analysis, functional principal component analysis, redundancy analysis, canonical coordinates, and correspondence analysis. The examination of his works shows that interdisciplinary collaboration and the utilization of real datasets were crucial in almost all of Rao's impactful contributions.
统计学家 C. R. Rao 在其职业生涯中对多元分析做出了许多贡献。他最早的一些贡献在近 80 年后的今天仍被继续使用和发扬光大，而他最近的贡献则推动了新的研究方向。本文将讨论这些贡献，它们如何帮助塑造了我们今天看到的多元分析，以及我们可以从回顾他的作品中学到什么。主题包括他对线性判别分析的扩展、Rao 的周长检验、Rao 的 U 统计量、Wilks 统计量的渐近展开、典型因子分析、函数主成分分析、冗余分析、典型坐标和对应分析。对其著作的研究表明，跨学科合作和对真实数据集的利用在拉奥几乎所有具有影响力的贡献中都至关重要。
期刊介绍：
The Scandinavian Journal of Statistics is internationally recognised as one of the leading statistical journals in the world. It was founded in 1974 by four Scandinavian statistical societies. Today more than eighty per cent of the manuscripts are submitted from outside Scandinavia.
It is an international journal devoted to reporting significant and innovative original contributions to statistical methodology, both theory and applications.
The journal specializes in statistical modelling showing particular appreciation of the underlying substantive research problems.
The emergence of specialized methods for analysing longitudinal and spatial data is just one example of an area of important methodological development in which the Scandinavian Journal of Statistics has a particular niche.
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