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Life and Work of C. R. RaoSat Gupta aa Department of Mathematics and Statistics , University of NorthCarolina at Greensboro , Greensboro, NC, 27402, USA

To cite this article: Sat Gupta (2007) Life and Work of C. R. Rao, Journal of Statistical Theory andPractice, 1:1, 141-146, DOI: 10.1080/15598608.2007.10411830

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Journal of © Grace Scientific Publishing Statistical Theory and Practice Volume 1, No. 1, March 2007

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Life and Work of C. R. Rao

Sat Gupta, Department of Mathematics and Statistics, University of North Carolina at Greensboro,

Greensboro, NC 27402, USA. Email: sngupta@uncg.edu

__________________________________________________________________________________________

On September 10, 1920, a small little boy, Calyampudi Radhakrishna Rao, was born in a small little village, Huvvinna Hadagalli, in southern India. Little did anyone know that 25 years later this little boy would arrive on the world statistics scene like a colossal personality whom the world would know as C. R. Rao . At a relatively young age of 25, when most researchers begin taking their first steps towards research, this little boy would have already made contributions that would prove to be the foundation stone for the theory of statistical inference.

Rao was born into an affluent family but his parents, C. Doraiswamy Naidu and A. Laxmikanthamma had no significant academic credentials. In fact his mother, A. Laxmikanthamma, had no formal schooling, as per the customs in southern India in those

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days. Yet, she raised Rao and his three brothers, Thippanna, Venkateswara and Ramachandra under a strict discipline. Going to school on time and doing well was part of this discipline. The girls did not go to school, as per the traditions. A more comprehensive account of Rao’s family background can be found in his biography by Krishnankutty (1996).

Rao grew up playing in the dusty streets of his village with his brothers and other friends. A common childhood game for Rao was one where you hit a small piece of wooden stick with a larger stick with the intention of sending the smaller stick as far as possible, and subsequently estimating and measuring the distance covered by the smaller stick. The little boy did not know that this estimation and measurement was going to become integral part of his life one day. During his early schooling, Rao had to change schools very frequently because his father was transferred from one place to another several times. Eventually, the family settled down in Vishakapatnam when Rao finished Grade 7. He finished his high school and also completed his first college degree from this city, always excelling in all subjects. After this, Rao joined Andhra University pursuing a B. A. (Honors) in mathematics, and completed it in 1940.

After completing B.A.(Hons) degree in mathematics, Rao wanted to pursue research in mathematics at Andhra University. However, his application for a scholarship to do research in mathematics was rejected since it was slightly late. This in spite of the fact that he got the first rank in B. A. (Honors). As fate would have it, Rao would later refuse an offer of Full Professorship from Andhra University. Also, the same Andhra University later conferred on Rao an honorary D.Sc. degree in mathematics. This was a major turning point in his life. After being refused the scholarship to do research in mathematics at Andhra University and not finding any appropriate job for being under-age, Rao joined a one year training program at the Indian Statistical Institute (ISI), Calcutta on January 1, 1941. This was the beginning of a long journey into the world of statistics. No one knows what would have happened if Rao had found an appropriate job when he needed one or got the scholarship to do research in mathematics at Andhra University.

Although Rao did not like the training program at ISI, he was very impressed with the research work carried out by the senior staff at ISI. Soon he joined a newly started master’s program in statistics at Calcutta University and completed it with distinction getting the first rank and record marks which is still unbroken. His master’s thesis at Calcutta University was rated by his external examiner as worthy of getting a Ph.D. degree in statistics. After completing the master’s degree in 1943, Rao joined ISI as a Technician, a rank offered to all junior statistics personnel at ISI. Simultaneously, he also accepted part-time lectureship at Calcutta University to teach statistics.

At ISI, he came in close contact with Professor P. C. Mahalanobis, who became his mentor and shaped his future. He also came in contact with other contemporary geniuses like R. C. Bose and S. N. Roy. Soon he began to impress everyone with his research work. So much so that Professor Mahalanobis started entrusting Rao with the editorial work of Sankhya, a statistics journal published from Calcutta. Rao had now settled down in Calcutta and was enjoying his teaching and research.

In early 1944, while teaching the concept of Fisher’s maximum likelihood estimation and its minimum asymptotic variance, a student, by the name of V. M. Dandekar, asked

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Life and Work of C. R. Rao 143

him if the result was also true for finite sample. This led to an Overnight Discovery that would later bear his name and would come to be known as Cramer-Rao Bound. Rao went home and worked on the student’s question for a few hours and got the answer by midnight. The result, along with many other results, appeared two years later in Rao (1945). Even today, Rao does not know how he got this result so quickly. It was like a miracle, something like what used to happen to Ramanujan, the legendry Indian mathematician, who used to say that God told him all the nice results while he was asleep and he simply jotted them down when he woke up.

In addition to this result, Rao included several other results in this landmark paper. One of these results was what is known today as Rao-Blackwell Theorem. Although Rao’s paper appeared in 1945 and Blackwell’s paper appeared in 1947, Berkson attributed the result to Blackwell and called the technique Blackwellization. When informed by Rao that his paper had appeared two years earlier, Berkson quickly agreed to change the term but told Rao that he would call the technique Rao-Blackwellization as Raoization would be “a bit too harsh on the tongue”. Rao did not have similar luck with another statistician, Lindely, who continued to give credit to Blackwell insisting that Rao did not realize the significance of this result as he did not mention this in the introduction of his paper. Rao’s response to Lindely was “This was only my first paper and I did not realize that some people read only the introduction to the paper and do not read what is proved inside the paper”. Part of the problem was that the journal, Bull. Cal. Math. Soc., which carried Rao’s paper, was not readily available at that time. Another aspect of this famous paper was that it discussed, for the first time, use of differential geometric methods. The significance of this discussion was fully realized some 30 years later and led to many statistical terms bearing Rao’s name. These include terms like Fisher-Rao metric, Rao distance, Rao measure and Cramer-Rao functional. It was truly astounding that by the age of 25, and without having a formal Ph. D. degree, Rao had already made everlasting contributions in statistics.

In August 1946, Rao was deputed by ISI to Cambridge at the request of Professor J. C. Trevor to work on an anthropological project using the methods developed at the Indian Statistical Institute. This had a profound impact not only on his professional career, but on his personal life as well. As per the customs in South India at the time, Rao was supposed to marry his mother’s brother’s daughter who was an uneducated girl. However, his mother’s brother did not want to wait for two years for Rao to come back and married off his daughter to some one else. This freed Rao from the customary obligation and upon his return from Cambridge he found a highly educated girl, Bhargavi, and married her in September 1948. They raised two kids – daughter Tejaswini and son Veerendra. On the professional side, Rao’s career at Cambridge flourished further under the guidance of the legendary R. A. Fisher. While working on the anthropological project, Rao derived significant statistical results that earned him a Ph. D. degree from Cambridge University in 1948. Later, Cambridge University awarded him the Sc. D. degree in 1965, based on his overall contributions to statistical theory and applications. Rao returned back to ISI in August 1948 and became a Full Professor at the young age of 28.

In another one of his early papers, Rao (1948) introduced what is known today as Rao’s Score Test. This test is termed as one of the Holy Trinity in testing, along with Likelihood Ratio Test and Wald Test. Yet another paper, Rao (1949), followed soon after and led to what are known today as Rao’s Orthogonal Arrays. Before reaching the age of 30, Rao

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had already made some of the most significant contributions to the theory of statistics. Many other contributions followed that led to important statistical terms bearing Rao’s name. These include terms like Geary-Rao Theorem, Hamming-Rao Bound, Kagan-Linnink-Rao Theorem, Lau-Rao Theorem, Rao’s Canonical Factor Analysis, Rao’s F-Test, Rao’s Quadratic Entropy, Rao-Rubin Theorem, Rao’s U-Test, and Rao-Yanoi Inverse.

Rao continued to work at ISI as the Head of The Research and Training School until 1972, as the Director until 1976, and as Jawaharlal Nehru Professor from 1976 until 1978. In 1978, he went to the Ohio State University as a Visiting Distinguished Professor. At this point, Rao was already planning to spend a life in retirement in India but in 1979, the University of Pittsburgh offered him the prestigious University Professorship and Rao moved to Pittsburgh to begin the second innings of his life. Retirement plans were put on hold and he stayed at Pittsburgh for the next 9 years establishing the Center of Multivariate Analysis and guiding ten more Ph. D. students. In 1988, Rao moved to the Pennsylvania State University as Eberly Professor of Statistics and has stayed there ever since.

During his illustrious career, 50 students have earned Ph. D. degrees under his supervision. He has authored or co-authored 14 books and over 400 research papers. He has received over 30 honorary degrees from universities in 18 countries, the most recent one from the New University of Lisbon in September 2006. For his pioneering contributions to statistical theory and applications, Rao has received numerous honors and awards. He has been elected to the National Academy of Sciences (USA), American Academy of Arts and Science, the Royal Society (UK), Indian National Science Academy, Lithuanian Academy of Sciences, and the Third World Academy of Sciences. He was made an Honorary Member of the International Statistical Institute, International Biometric Society, Royal Statistical Society (UK), Finnish Statistical Society, Portuguese Statistical Society, Institute of Combinatorics and Applications, and World Innovation Foundation. He was also made Honorary Life Fellow of King’s College, Cambridge, UK. He has been the President of many prestigious statistical associations such as the International Statistical Institute, Institute of Mathematical Statistics, USA and the International Biometric Society. He was inducted into the Hall of Fame of the National Institution for Quality and Reliability, Chennai Branch, for his contributions to industrial statistics and the promotion of quality control programs in Indian industries. At the Berlin conference of the International Statistical Institute held in 2003, Rao received the prestigious International Mahalanobis Prize “for lifetime achievement in statistics and the promotion of best statistical practice”.

He has received numerous medals. These include the Gold Medal of Calcutta University, Wilks Medal of the American Statistical Association, Wilks Army Medal, Guy Medal in Silver of the Royal Statistical Society, Megnadh Saha Medal and Srinivasa Ramanujan Medal of the Indian National Science Academy, J. C. Bose Gold Medal of Bose Institute and Mahalanobis Centenary Gold Medal of the Indian Science Congress. In 2002, he received National Medal of Science, USA, from President George Bush “for his pioneering contributions to the foundations of statistical theory and multivariate statistical methodology and their applications, enriching the physical, biological, mathematical, economic and engineering sciences”. In his compilation of ‘Figures from the History of Probabiliuty and Statistics’, John Aldrich (http://www.economics.soton.ac.uk/staff/

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ldrich/Figures.htm) lists 35 legendray figures in Probability and Statistics for the period 1650-2000. C. R. Rao is the only one listed there who is still alive.

The Government of India has honored him with the second highest civilian award, Padma Vibhushan for “outstanding contributions to Science and Engineering / Statistics”, and also instituted a cash award in his honor “to be given once in two years to a young statistician for work done during the preceding 3 years in any field of statistics”.

Rao is now retired from Eberly Professorship at Penn State, but people like Rao never really retire. He continues to maintain an active research agenda as Eberly Professor Emeritus of Statistics and Director of the Center for Multivariate Analysis at the Pennsylvania State University. He continues to travel widely giving traditional research lectures and lectures of philosophical nature such as the one on “Has statistics a future? If so, in what form?” given at the International Conference on Interdisciplinary Mathematical & Statistical Techniques, held at Polytechnic Institute of Tomar, Portugal, September 1-4, 2006. Rao feels that the current statistical methodology based on simple probabilistic models may be inadequate in the present millennium dominated by information technology. He feels that “machine learning” methods such as “data mining” can no longer be neglected by the statisticians and that algorithmic research will play an important role in statistics.

Currently Rao spends about 5 months in a year in India in developing C. R. Rao Advanced Institute for Mathematics, Statistics and Computer Science, an institute named after Rao and established on the campus of the University of Hyderabad, with support from the Government and private donations. For the foundation stone laying ceremony for the Center on February 20, 2007, the United States President, George Bush, sent a congratulatory message that read “… The vision of the C.R. Rao Institute is to promote education and research and to foster international scientific collaboration. Those who have made this institute possible and those who will serve within its walls are helping to advance knowledge and enhance the lives of people everywhere. I appreciate Dr. Rao, Hyderabad University, and all those who use their abilities in the spirit of discovery and international goodwill. Your commitment to excellence in education and innovation sets a fine example and inspires others to seize the unprecedented opportunities before us. Laura and I send our best wishes. May God bless you.” In a similar message, the Indian Prime Minister, Honorable Mr Manmohan Singh said, “… The Institute bears the name of an outstanding scholar who has excelled in the field of mathematics and statistics and dedicated himself to the promotion of basic research in our country. Professor C.R.Rao’s life and work are a source of great inspiration to researchers and scholars all over the world. I hope that the institute will fulfil Prof. Rao’s vision and carry forward his mission of using basic research for solving the social and economic problems of our country. I wish this endeavour all success”

Rao says that his retirement enables him to spend some time with the family, especially with the grandchildren, Amar and Rohith. He also finds time to visit his son Veerender Rao, a Computer Consultant in Pittsburgh and his daughter, Dr. Tejaswini Rao, Professor of Nutrition at Suny College in Buffalo.

We hope and pray that Rao continues to enjoy good health and continues to provide guidance to the younger generation for years to come.

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Acknowledgements

In this article, I have quoted liberally from Krishnankutty (1996) and from personal notes sent by Professor Rao.

References

Krishnankutty, N., 1996. Putting Chance to Work – a Biography of C. R. Rao. State College, PA, USA. Rao, C.R., 1945. Information and Accuracy Attainable in the Estimation of Statistical Parameters. Bull. Cal.

Math. Soc. 37, 81-91. Rao, C.R., 1948. Large Sample Tests of Statistical Hypothesis Concerning Several Parameters with Application

to Problems of Estimation. Proc. Camb. Philos. Soc. 44, 50-57. Rao, C.R., 1949. On a Class of Arrangements. Edin. Math. Proc. 8, 119-125.

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