Looking back: Selected contributions by C. R. Rao to multivariate analysis

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.