C.R. Rao wins top statistics award – a look back at his pioneering work

The Indian-American statistician C.R. Rao has been awarded the 2023 International Prize in Statistics. His work has influenced “economics, genetics, anthropology, geology, national planning, demography, biometry, and medicine”.

The Indian-American statistician Calyampudi Radhakrishna Rao has been awarded the 2023 International Prize in Statistics, which is statistics’ equivalent of the Nobel Prize. It was established in 2016 and is awarded once every two years to an individual or team “for major achievements using statistics to advance science, technology and human welfare.”

Prof. Rao, who is now 102 years old, is a ‘living legend’ whose work has influenced, in the words of the American Statistical Association, “not just statistics” but also “economics, genetics, anthropology, geology, national planning, demography, biometry, and medicine”. The citation for his new award reads: “C.R. Rao, a professor whose work more than 75 years ago continues to exert a profound influence on science, has been awarded the 2023 International Prize in Statistics.”

Rao’s groundbreaking paper, ‘Information and accuracy attainable in the estimation of statistical parameters’, was published in 1945 in the Bulletin of the Calcutta Mathematical Society, a journal that is otherwise not well known to the statistics community. The paper was subsequently included in the book Breakthroughs in Statistics, 1890-1990.

This was an impressive achievement given Rao was only 25 at the time and had just completed his master’s degree in statistics two years prior.

He would go on to do his PhD in 1946-1948 at King’s College, Cambridge University, under the supervision of Ronald A. Fisher, widely regarded as the father of modern statistics.

The Cramér-Rao inequality is the first of the three results of the 1945 paper. When we are estimating the unknown value of a parameter, we must be aware of the estimator’s margin of error. Rao’s work provided a lower limit on the variance of an unbiased estimate for a finite sample. The result has since become a cornerstone of mathematical statistics; researchers have extended it in many different ways, with applications even in quantum physics, signal processing, spectroscopy, radar systems, multiple-image radiography, risk analysis, and probability theory, among other fields.

In an article published in the journal Statistical Science in 1987, the American statistician Morris H. DeGroot set out an intriguing story (corroborated by Rao’s own account) of how Rao arrived at the lower limit. Prof. Fisher had already established an asymptotic (i.e. when the sample size is very large) version of the inequality, and it seems a student had asked Rao, “Why don’t you prove it for finite samples?” in 1944. A then-24-year-old Rao did so in under 24 hours!