Dr. C.R. Rao Wins Top Statistics Award a look back at his pioneering work

Dr. Calyampudi Radhakrishna Rao, FRS, alias C.R. Rao, was an Indian-American mathematician and statistician. He was an emeritus professor at Pennsylvania State University, and Research Professor at the University at Buffalo. He has authored many books and over 300 research papers that have been published in reputed journals.

Dr. C.R. Rao hails from Hadagali, Karnataka. He completed his schooling in several places like Gudur, Nuzvid, Nandigama, and Visakhapatnam, Andhra Pradesh. He holds degrees in MSc Mathematics, MA Statistics and Ph.D. In the beginning, he worked at the Indian Statistical Institute and also at the Anthropological Museum in Cambridge. Later on in his life, he held several important positions such as Director of the Indian Statistical Institute and as a University Professor at the University of Pittsburgh and also at Indian Universities.

The first award he received came from the UK, it was the Fellowship of The Royal Society [FRS], in 1967. The Government of India honoured him with Padma Bhushan (1968) and Padma Vibhushan (2001). He was awarded the Indian Science Prize in 2010

At the age of sixty and went to live with his daughter and grandchildren who live in the United States of America.

At the age of 62, he became a professor of statistics at the University of Pittsburgh and at the age of 70, he became the head of the department at the University of Pennsylvania. He received US citizenship at the age of 75 and the National Medal for Science at the age of 82, a White House honour. At the age of 102, he received the International Prize in Statistics, which is the Statistics equivalent of the Nobel Prize.

The International Prize in Statistics 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. Raos 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.

The early research of Dr. C.R Rao

Raos ground-breaking paper, Information and accuracy attainable in the estimation of statistical parameters, was published in 1945 in theBulletin of the Calcutta Mathematical Society, a journal that is otherwise not well known to the statistics community. The paper was subsequently included in the bookBreakthroughs in Statistics, 1890-1990.

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

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

The Cramr-Rao inequality was 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 estimators margin of error. Raos 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 journalStatistical Sciencein 1987, the American statistician Morris H. DeGroot set out an intriguing story (corroborated by Raos 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 dont you prove it for finite samples? in 1944. A then-24-year-old Rao did so in under 24 hours!

The second outcome of the 1945 paper was the Rao-Blackwell Theorem, which offers a method to improve an estimate to anoptimalestimate. The Rao-Blackwell theorem and the Cramr-Rao inequality are both related to the quality of estimators.

A new interdisciplinary area called information geometry was born as a result of the papers third finding. This field integrated principles from differential geometry into statistics, including the concepts of metric, distance, and measure. Erich L. Lehmann, a renowned statistician, said in 2008 that &this work [of Raos] was before its time and came into its own only in the 1980s.

So overall, Raos 1945 paper made an outstanding contribution, boosting the development of modern statistics and its widespread application in modern research. In a 2008 book,Reminiscences of a Statistician: The Company I Kept, Lehmann also discussed the generative nature of the paper i.e. the goldmine of insights that it was and acknowledged that &several of my early papers grew out of Raos paper of 1945.

Going back even further ! How did Rao enter the field of statistics?

The Australian statistician Terry Speed claimed that the &1940s were ungrudgingly C.R. Raos. His 1945 paper & will guarantee that, even had he done nothing else but there was much else.

Indeed, one of Raos papers in 1948 offered a novel generic approach to testing hypotheses, now widely known as the &Rao score test. In fact, the three test procedures the likelihood ratio test of Jerzy Neyman and E.S. Pearson (1928), the Wald test (1943) of Abraham Wald, and the Rao score test (1948) are sometimes called &the holy trinity of this branch of statistics.

Rao also contributed to orthogonal arrays, a concept in combinatorics that is used to design experiments whose results are qualitatively good, as early as 1949. A 1969Forbesarticle described it as &a new mantra in industrial establishments.

Given the magnitude and relevance of his contributions, it might seem surprising that Rao entered the field of statistics by chance.

Despite scoring first in mathematics at Andhra University, a 19-year-old Rao didnt secure a scholarship there for administrative reasons. He was also rejected for a mathematicians job at an army survey unit because he was judged to be too young.

When he was staying at a hotel in Calcutta, he met a man who was employed in Bombay and had been sent to Calcutta to be trained at the Indian Statistical Institute. He asked Rao to apply to the institute as well. Rao did so, for a year-long training programme in statistics, hoping the additional qualification would help him land a job.

P.C. Mahalanobis, then director of the institute, replied promptly and Rao was enrolled. That marked the beginning of a four-decade-long stay at the institute. Rao retired in 1979 and afterwards settled in the U.S.

The first half of the 20th century was the golden period of statistical theory in general, and Rao is undoubtedly one of the reasons for this being the case, thanks to his mathematical ingenuity. In the words of the late mathematician Samuel Karlin, Raos contributions to statistical theory have &earned him a place in the history of statistics.

Indian statisticians also owe Prof. Rao gratitude for his enormous contributions to the growth of statistics in the country, notably at the Indian Statistical Institute (where this author works). As Lehmann wrote, Rao was &the person who did the most to continue Mahalanobiss work as a leader of statistics in India.

Death

C. R. Rao died at Buffalo, New York, U.S., on 23 August 2023, at the age of 102.

Mr. T. Dhasaratharaman

Assistant Manager – Statistician

Dr. C.R. Rao Wins Top Statistics Award a look back at his pioneering work