It was 1944. The lecturer at the Indian Statistical Institute (ISI) in Calcutta, as it was called then, was explaining an important result on the variance of the estimate (the smaller the variance, the better the estimate) of a population characteristic from a number of sample observations. R A Fisher, the father of modern statistics, had demonstrated that there is a lower limit to the variance of the estimate in whatever way one might estimate, depending on a certain measure of information in the sample. He considered his sample size to be large. However, in real life one often has to work with small samples due to various factors like cost, availability of data et cetera.
One student raised an interesting question. Would Fisher's result hold when the sample size was small, which is the case facing many research workers in many fields? The lecturer said that he would try to get the answer. On going home that night, he worked out the solution and gave the answer the next day! Soon he realised that his result held good for a number of other cases also involving small samples. The teacher was Calyampudi Radhakrishna Rao, the global doyen of statistics, and the student was V M Dandekar, who went on to become an eminent economist and head of the Gokhale Institute of Politics and Economics in Pune.
The result came to be known as Cramer-Rao Inequality, a fundamental contribution with applications in many fields. Cramer, a leading probabilist of Sweden, had also worked on similar lines. But Rao had found out the result earlier than him. It was World War II and, due to delays in publication, his article could be published only in 1945. Rao was around 23 years old when he statistically proved the above-mentioned result. Soon he was to gain repute internationally for his association with many new statistical ideas - a feat that belied his young age. (See Contributions, Awards and Honours)
Rao received his PhD from Cambridge University in 1948 with Fisher as his mentor. He worked at ISI for 40 years before taking mandatory retirement as the director at the age of 60. He created the image of ISI as a world-class training and research centre for statistics on the strong foundation laid by the renowned P C Mahalanobis. He then moved to the US and worked for the University of Pittsburgh and the Pennsylvania State University, where he continues to be Professor Emeritus.
Born on September 10, 1920, 93-year-old Rao has managed to accomplish just as much after his retirement as during his tenure at ISI. He is a true polymath whose interests extend beyond the world of numbers over a large field of knowledge. He is a real philosopher in its original meaning ('lover of wisdom or knowledge').
A multi-tasker, he managed to work on various collaborations simultaneously. For instance, Rao worked with Fisher on mapping the chromosomes of mice even as he was collaborating with an anthropologist in studying bones from ancient graves - 1,000-years-old brought by a British expedition to the Anthropological Museum in London.
The American Statistical Association has described him as "a living legend whose work has influenced not just statistics, but has had far-reaching implications for fields as varied as economics, genetics, anthropology, geology, national planning, demography, biometry, and medicine." But while adding a long list of accomplishments to his credit, it has left out his interests in cooking, gardening, photography and Indian classical music and dances. Not many know that he also established a school for teaching Kuchipudi in New Delhi.
Rao's advice to economists: "Probably what is wrong with economists is that they are not trying to refine their measurements or trying to measure new variables which cause economic changes. That is far more important than dabbling with whatever the data available and trying to make predictions based on them. So there is a lot of work that needs to be done in the soft sciences such as psychology and economics." ('A Conversation with C R Rao, Morris H DeGroot', Statistical Science, Vol.2, No. 1,)
He was honoured with the Padma Vibhushan in 2001 at a time when he had achieved enough to be made a Bharat Ratna, an honour of which he is completely deserving. More importantly, he is eminently qualified for the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel. In the first place, his contributions have impacted economics and econometrics as much as they have done other disciplines. Secondly, the prize is no longer limited to economics but extended to other social sciences also. Stark examples of this are John Nash, a mathematician, who received it for his contribution to Game Theory (1994), and Daniel Kahneman, a professor of psychology (2002). One hopes that Indian economists will canvass Rao's name among the members of the nominating or electoral college of the international economic community. The process of nominations started in September and the end of January 2014 is the closing date for the Nobel Foundation to receive the nomination forms.
CONTRIBUTIONS, AWARDS AND HONOURS
At last count, Rao had written 14 books and 350 articles and reports. Three of his books have been translated into Chinese and Japanese and several European languages. His book Linear Statistical Inference and its Application (1973) may be found in the libraries of econometricians, among others, for whom it is the Bible.
According to the Social Science Citation Index it is the most cited book in econometric literature.
The following concepts and theories are associated with Rao: Cramer-Rao Inequality, Rao-Blackwellization, Rao's Score Test, Fisher-Rao and Rao Theorems on second order efficiency of an estimator, …. The list is endless. Cramer- Rao Bound has been used in Quantum Physics while Rao-Blackwellization has found applications in adaptive sampling, particle filtering in high-dimensional state spaces, dynamic Bayesian networks, et cetera. His results have led to contributions of strategic significance to signal detection, tracking of non-friendly planes and recognition of objects by shape.
Rao has received over 38 honorary doctoral degrees from universities in 19 countries around the world and numerous awards and medals for his contributions to Statistics and science.
He is a member of eight National Academies in India, UK, US and Italy. He was awarded the United States National Medal of Science - the nation's highest award for lifetime achievement in the field of scientific research - in June 2002. He was the recipient of the India Science Award for 2010, the highest honour conferred by the Government of India in the scientific domain. Innumerable are the medals received by him including those for his first-class-first performances as a student.
One of the two highly cherished honours was the Fellowship of the Royal Society in 1967, as he was the sixth living Indian to receive it, the others being C V Raman, S N Bose, D N Wadia, T R Seshadri and P C Mahalanobis. Earlier S Ramanujan and J C Bose had been honoured thus. A proud moment for him was when, on being inducted as a Life Fellow of King's College at Cambridge in 1974, he was escorted to his room across the front lawn, an exclusive privilege enjoyed only by the Fellows. When he had been a student there he had to walk on the side paths. The Life Fellowship is limited to 11 persons at any time. A new Fellow is admitted when a vacancy arises due to the death of another Fellow.
He has been the President of many professional societies and institutes. He established the Indian Econometric Society. The C R Rao Advanced Institute of Mathematics, Statistics and Computer Science has also been set up in Hyderabad in his honour.
One student raised an interesting question. Would Fisher's result hold when the sample size was small, which is the case facing many research workers in many fields? The lecturer said that he would try to get the answer. On going home that night, he worked out the solution and gave the answer the next day! Soon he realised that his result held good for a number of other cases also involving small samples. The teacher was Calyampudi Radhakrishna Rao, the global doyen of statistics, and the student was V M Dandekar, who went on to become an eminent economist and head of the Gokhale Institute of Politics and Economics in Pune.
The result came to be known as Cramer-Rao Inequality, a fundamental contribution with applications in many fields. Cramer, a leading probabilist of Sweden, had also worked on similar lines. But Rao had found out the result earlier than him. It was World War II and, due to delays in publication, his article could be published only in 1945. Rao was around 23 years old when he statistically proved the above-mentioned result. Soon he was to gain repute internationally for his association with many new statistical ideas - a feat that belied his young age. (See Contributions, Awards and Honours)
* * * * *
Rao received his PhD from Cambridge University in 1948 with Fisher as his mentor. He worked at ISI for 40 years before taking mandatory retirement as the director at the age of 60. He created the image of ISI as a world-class training and research centre for statistics on the strong foundation laid by the renowned P C Mahalanobis. He then moved to the US and worked for the University of Pittsburgh and the Pennsylvania State University, where he continues to be Professor Emeritus.
Born on September 10, 1920, 93-year-old Rao has managed to accomplish just as much after his retirement as during his tenure at ISI. He is a true polymath whose interests extend beyond the world of numbers over a large field of knowledge. He is a real philosopher in its original meaning ('lover of wisdom or knowledge').
A multi-tasker, he managed to work on various collaborations simultaneously. For instance, Rao worked with Fisher on mapping the chromosomes of mice even as he was collaborating with an anthropologist in studying bones from ancient graves - 1,000-years-old brought by a British expedition to the Anthropological Museum in London.
The American Statistical Association has described him as "a living legend whose work has influenced not just statistics, but has had far-reaching implications for fields as varied as economics, genetics, anthropology, geology, national planning, demography, biometry, and medicine." But while adding a long list of accomplishments to his credit, it has left out his interests in cooking, gardening, photography and Indian classical music and dances. Not many know that he also established a school for teaching Kuchipudi in New Delhi.
* * * * *
Rao's advice to economists: "Probably what is wrong with economists is that they are not trying to refine their measurements or trying to measure new variables which cause economic changes. That is far more important than dabbling with whatever the data available and trying to make predictions based on them. So there is a lot of work that needs to be done in the soft sciences such as psychology and economics." ('A Conversation with C R Rao, Morris H DeGroot', Statistical Science, Vol.2, No. 1,)
He was honoured with the Padma Vibhushan in 2001 at a time when he had achieved enough to be made a Bharat Ratna, an honour of which he is completely deserving. More importantly, he is eminently qualified for the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel. In the first place, his contributions have impacted economics and econometrics as much as they have done other disciplines. Secondly, the prize is no longer limited to economics but extended to other social sciences also. Stark examples of this are John Nash, a mathematician, who received it for his contribution to Game Theory (1994), and Daniel Kahneman, a professor of psychology (2002). One hopes that Indian economists will canvass Rao's name among the members of the nominating or electoral college of the international economic community. The process of nominations started in September and the end of January 2014 is the closing date for the Nobel Foundation to receive the nomination forms.
CONTRIBUTIONS, AWARDS AND HONOURS
At last count, Rao had written 14 books and 350 articles and reports. Three of his books have been translated into Chinese and Japanese and several European languages. His book Linear Statistical Inference and its Application (1973) may be found in the libraries of econometricians, among others, for whom it is the Bible.
According to the Social Science Citation Index it is the most cited book in econometric literature.
The following concepts and theories are associated with Rao: Cramer-Rao Inequality, Rao-Blackwellization, Rao's Score Test, Fisher-Rao and Rao Theorems on second order efficiency of an estimator, …. The list is endless. Cramer- Rao Bound has been used in Quantum Physics while Rao-Blackwellization has found applications in adaptive sampling, particle filtering in high-dimensional state spaces, dynamic Bayesian networks, et cetera. His results have led to contributions of strategic significance to signal detection, tracking of non-friendly planes and recognition of objects by shape.
Rao has received over 38 honorary doctoral degrees from universities in 19 countries around the world and numerous awards and medals for his contributions to Statistics and science.
He is a member of eight National Academies in India, UK, US and Italy. He was awarded the United States National Medal of Science - the nation's highest award for lifetime achievement in the field of scientific research - in June 2002. He was the recipient of the India Science Award for 2010, the highest honour conferred by the Government of India in the scientific domain. Innumerable are the medals received by him including those for his first-class-first performances as a student.
One of the two highly cherished honours was the Fellowship of the Royal Society in 1967, as he was the sixth living Indian to receive it, the others being C V Raman, S N Bose, D N Wadia, T R Seshadri and P C Mahalanobis. Earlier S Ramanujan and J C Bose had been honoured thus. A proud moment for him was when, on being inducted as a Life Fellow of King's College at Cambridge in 1974, he was escorted to his room across the front lawn, an exclusive privilege enjoyed only by the Fellows. When he had been a student there he had to walk on the side paths. The Life Fellowship is limited to 11 persons at any time. A new Fellow is admitted when a vacancy arises due to the death of another Fellow.
He has been the President of many professional societies and institutes. He established the Indian Econometric Society. The C R Rao Advanced Institute of Mathematics, Statistics and Computer Science has also been set up in Hyderabad in his honour.