C.R. Rao shaped the dramatic growth of mathematical statistics in the 20th century, refining and restructuring it from its somewhat ad hoc origins
Stephen Stigler, a historian of statistics, proposed the law that no scientific discovery is named after its original discoverer. While there is the tiniest bit of exaggeration in Stigler’s law of eponymy, Calyampudi Radhakrishna Rao would perhaps concur with his colleague’s judgment. The statistical test used extensively in econometrics, widely known as Lagrange multiplier test, was developed by Professor Rao in 1947. This is not recognised even by most Indian econometricians. Nor is he widely recognised by the general public of our country as he deserves to be.
Standing at the cusp of an age of big data, data analytics, machine learning, bioinformatics and artificial intelligence, we have more reasons to honour and celebrate Professor Rao’s contributions and achievements. Along with a handful of others such as Egon Pearson, Ronald Fisher, Andrey Kolmogorov, and Jerzy Neyman, he shaped the dramatic growth of mathematical statistics in the 20th century, refining and restructuring it from its somewhat ad hoc origins, making this new age possible. And it is remarkable that he is almost entirely a “product of India” — as the website of the C.R. Rao Advanced Institute of Mathematics, Statistics and Computer Science, affiliated to the University of Hyderabad, says. He turns 100 on September 10 and continues to guide and inspire students and practitioners of statistics as he has for the past eight decades.
Calyampudi Radhakrishna Rao was born as the eighth child of C.D. Naidu and A. Laxmikanthamma in the small town of Huvina Hadagali in present-day Karnataka (in erstwhile Madras province). He was an exceptionally good student, and completed a BA (Hons.) degree in Mathematics from Andhra University with distinction and first rank. He hoped to obtain a scholarship for higher studies in mathematics, but was unable to achieve this goal. The Second World War had commenced by that time, and he decided to apply for a job in the survey unit of the Army in North Africa. He visited Calcutta (as it was then called) for this purpose, but he did not qualify for the job. Destiny, in the form of one of his friends, took him to the nascent Indian Statistical Institute; the legendary Prasanta Chandra Mahalanobis had established the institute 10 years earlier. The young C.R. Rao joined a training programme offered by the ISI.
In 1943, Professor Rao completed his MA in Statistics from Calcutta University, again with a first rank. By the age of 22, he had already published seven technical papers in mathematical statistics. Mahalanobis recognised the potential of this young man, and C.R. Rao was deputed to Cambridge University in 1946 to assist in the analysis of some anthropological data. While he was at Cambridge, he registered for a doctoral degree under the guidance of the celebrated Professor Ronald A. Fisher. He returned to the ISI in 1948 after being awarded his Ph.D. and was appointed professor there the following year.
Professor Rao spent more than three-and-a-half decades at the ISI, and he served the institution in various capacities: as the Head and Director of the Research and Training School of the ISI, as the Jawaharlal Nehru Professor of the Institute and so on. In 1972, he succeeded Mahalanobis as the Director. Professor Rao thus played a key role in building the worldwide reputation of the ISI. In a speech at the institute, Professor Fisher once pointed out that more than half the qualified statisticians working in the world were Indians, for quite some time. Most of them were Professor Rao’s students.
On his retirement from the ISI in 1979, he joined the University of Pittsburgh as Professor and later shifted to Pennsylvania State University as the Eberly Family Chair Professor of Statistics. He served as the Director of the Center for Multivariate Analysis at Penn State until 2008. One statistic about this statistician is just astounding: he published over 270 journal articles since his retirement from the Indian Statistical Institute.
It is scarcely possible to describe the contours of Professor Rao’s research output in an article such as this one. We will touch upon a few preeminent results from his oeuvre. In 1922, Professor Fisher had defined a metric which conveys the amount of information that a sample can provide about the value of an unknown population parameter. Professor Rao (and Harald Cramér, independently) proved that any unbiased estimator of the parameter had to have a variance greater than the reciprocal of the Fisher metric. This is the well-known Cramér-Rao lower bound, one of Professor Rao’s most renowned contributions. This result, and the famous Rao-Blackwell theorem (independently discovered by D.H. Blackwell), appeared in a celebrated paper that Professor Rao published in 1945 — when he was only 24. As mentioned earlier, in a 1947 paper, Professor Rao introduced Rao’s Score Test; this test has certain practical advantages over the two other commonly used tests for the same purpose — the Wald test and the likelihood-ratio test.
Asked by Frank Nielsen of the Ecole Polytechnique (France) as to his three major contributions, Professor Rao listed orthogonal arrays (OAS) and quadratic entropy (QE) other than the score statistic as the main ones. OAS was subsequently used by Genichi Taguchi of Japan, to develop the well-known Taguchi methods to improve the quality of manufactured goods. QE is a perfect diversity measure that can be used to carry out analysis of diversity (ANODIV) of any order.
As India started building its institutional infrastructure after Independence, Professor Rao was instrumental in setting up our national statistical framework. During the 1960s, he served as Chairman of the Committee on Statistics of the Government of India. He also chaired the Committee on Mathematics of the Atomic Energy Commission and was a member of the Committee on Science and Technology. He was the moving force behind the International Statistical Educational Centre (ISEC) at the ISI, where students and government statisticians from developing countries could learn the techniques of statistics and the methods for establishing their national statistical bureaus. Statistics, as we all know today, is an indispensable tool in areas as varied as economics, psychology, management and epidemiology. Professor Rao foresaw this development and established units in ISI to train statisticians in these various applied disciplines.
He had the reputation of being an exemplary teacher. Asked about the biggest achievement in his life, he was quick to reply that it was the outstanding contributions his students were making to statistical theory and practice. He has supervised 50 students in their doctoral research. He was mentor, and colleague as well in some cases, to many outstanding mathematical statisticians and mathematicians. The late Debabrata Basu, who was Professor at ISI and subsequently at Florida State University, is one of them. S.R. Srinivasa Varadhan (aka Raghu Varadhan), Professor at the Courant Institute of Mathematical Sciences in New York and winner of the Abel Prize in 2007, is another. Others such as R. Ranga Rao, K.R. Parthasarathy and the late V.S. Varadarajan are some among the many distinguished academics mentored by Professor Rao.
Awards and accolades
He has been the recipient of countless awards and accolades. He was honoured with the Padma Vibhushan in 2001. The then President of the United States, George W. Bush, conferred the National Medal of Science on him in 2002. He received the Shanti Swarup Bhatnagar Award from Prime Minister Nehru in 1963. The American Statistical Association awarded him the Samuel S Wilks Memorial Award in 1989. In 2011, he became the first non-European and non-American to receive the Guy Medal in Gold from the Royal Statistical Society of the United Kingdom. Professor Rao has been bestowed with 38 honorary doctoral degrees from universities located in 19 different countries.
The extent to which a society recognises and celebrates its true heroes is an indicator of the cultural and institutional climate it has built to produce, retain, and nurture its talent. In our recent history, India has produced very few scientists whose output can rival that of Professor Rao. He deserves to be known, appreciated, and celebrated by every citizen of the country. Barely a week after celebrating Teacher’s Day, on the occasion of his 100th birthday, we offer our humble tribute to this peerless teacher, academic and institution builder. Prof. Rao currently lives in the city of Buffalo, in New York State, with his daughter Tejaswini’s family. The inspiration he provides should, and indeed will, live in the hearts of every Indian.