As the Indian-American statistician Prof. CR Rao passed away, it’s time to pay tribute to a legendary academic by a 50-year junior to him at Calcutta University’s statistics master’s programme. In fact, when, in September 2020, the statistics world celebrated the centenary of Prof. Rao, I thought of writing an article on the life and career of the legend for the benefit of the common reader. But it was a difficult task to convince the opinion editors at that time.

The situation has changed considerably in three years. Rao has now been awarded the 2023 International Prize in Statistics, which may be viewed as the statistical science equivalent of the Nobel Prize, Abel Prize, or Turing Award. This award is relatively new and was established in 2016. Every two years, an individual or team receives this honour “for major achievements using statistics to advance science, technology and human welfare.” Rao is certainly a product of the Indian academic system, and most of his pioneering research was done during his four-decade-long stay at the Indian Statistical Institute.

Breakthrough research

However, it’s not that Rao has made a significant contribution between 2020 and 2023 to get this award; rather, it’s a recognition of one of his breakthrough research papers, published in 1945 in the Bulletin of the Calcutta Mathematical Society. Rao was 25 at the time, and the research for the paper was done when he was just 24. In fact, he had just completed his master’s in statistics two years prior and would do his PhD later on, during 1946-1948, at King’s College, Cambridge University.

This 1945 “breakthrough” paper, in fact, is a remarkable piece of research that included three extraordinarily brilliant contributions, any of which had the potential to make a research publication a “classic.” Two of the results, the Cramér-Rao inequality and the Rao-Blackwell theorem, are now part of the undergraduate syllabus in statistics worldwide, and the third one was an idea given before its time and pioneered a new interdisciplinary area called “information geometry,” an area that eventually flourished in the 1980s.

But this, certainly, was not the only significant research work that Rao did. In fact, Rao gave an interview to Prof. Frank Nielsen, a professor of computer science at École Polytechnique, France, in 2016. Interestingly, when asked to describe three of his major contributions to statistics, Prof. Rao mentioned “orthogonal arrays,” “score statistic,” and “quadratic entropy”, which have received wide applications. The first two of these major contributions were also done in the 1940s, when Rao was under 30!

Interestingly, Rao didn’t consider any of the three pioneering ideas for his Nobel-like prize among his three most prominent contributions in statistics! His “score test” is also included in today’s undergraduate syllabus in statistics. This, along with two other well-known statistical test procedures — the likelihood ratio test and the Wald test — is sometimes referred to as “the holy trinity.” Orthogonal arrays, which Rao contributed to as early as 1949, were described as “a new mantra” in a variety of industrial establishments in a 1969 Forbes article. In fact, CR Rao is known as the “Scientist’s Statistician,” and some of his statistical tests and other contributions continue to guide scientists all over the globe.

Rao was a close aide to Prof. PC Mahalanobis and eventually succeeded him in running the Indian Statistical Institute (ISI) as well. Rao, of course, settled in the US after his retirement from the institute. But he continued to do serious research, and he never retired from academics.

Thus, a remembrance of CR Rao’s academic legacy is the most appropriate way to bid adieu to him. And, to our utmost pride, that reminiscence is a celebration of the Indian academic system and its strong statistical heritage as well. It is certainly one of the best fruits of the statistical culture in the country, whose seed was sown and nourished by Prof. Prasanta Chandra Mahalanobis.

The writer is Professor of Statistics, Indian Statistical Institute, Kolkata

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