C. R. Rao
C. R. Rao  

Prof. Rao at Indian Statistical Institute, Chennai in April 2012


Born  Hadagali, Kingdom of Mysore, British India 
10 September 1920
Residence  India, United Kingdom, United States 
Citizenship  United States^{[1]} 
Fields  Mathematics and statistics 
Institutions  Indian Statistical Institute Cambridge University Penn State University University at Buffalo 
Alma mater  Andhra University University of Calcutta King's College, Cambridge 
Thesis  Statistical Problems of Biological Classifications (1948) 
Doctoral advisor  Ronald Fisher 
Doctoral students  
Known for  Cramér–Rao bound Rao–Blackwell theorem Orthogonal arrays Score test 
Notable awards  Padma Vibhushan National Medal of Science (2001) S. S. Bhatnagar Prize Guy Medal (Silver 1965, Gold 2011) 
Calyampudi Radhakrishna Rao, FRS known as C R Rao (born 10 September 1920) is an Indianborn, naturalized American, mathematician and statistician. He is currently professor emeritus at Penn State University and Research Professor at the University at Buffalo. Rao has been honoured by numerous colloquia, honorary degrees, and festschrifts and was awarded the US National Medal of Science in 2002.^{[2]} 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."^{[2]} The Times of India listed Rao as one of the top 10 Indian scientists of all time.^{[3]} Rao is also a Senior Policy and Statistics advisor for the Indian Heart Association nonprofit focused on raising South Asian cardiovascular disease awareness.^{[4]}
Contents
Early life
C R Rao was born in Hadagali, Bellary, Karnataka, India. He received an M.Sc. in mathematics from Andhra University and an M.A. in statistics from Calcutta University in 1943.^{[2]} He was among the first few people in the world to hold a master's degree in Statistics.^{[citation needed]}
Academic career
Rao worked at the Indian Statistical Institute and the Anthropological Museum in Cambridge before acquiring a Ph.D. degree at King's College in Cambridge University under R. A. Fisher in 1948, to which he added a Sc.D. degree, also from Cambridge, in 1965.
He held several important positions, as the Director of the Indian Statistical Institute, Jawaharlal Nehru Professor and National Professor in India, University Professor at the University of Pittsburgh and Eberly Professor and Chair of Statistics and Director of the Center for Multivariate Analysis at the Pennsylvania State University. As Head and later Director of the Research and Training School at the Indian Statistical Institute for a period of over 40 years, Rao developed research and training programs and produced several leaders in the field of Mathematics. On the basis of Rao's recommendation, the ASI (The Asian Statistical Institute) now known as Statistical Institute for Asia and Pacific was established in Tokyo to provide training to statisticians working in government and industrial organizations.^{[5]}
Among his bestknown discoveries are the Cramér–Rao bound and the Rao–Blackwell theorem both related to the quality of estimators. Other areas he worked in include multivariate analysis, estimation theory, and differential geometry. His other contributions include the Fisher–Rao Theorem, Rao distance, and orthogonal arrays. He is the author of 14 books and has published over 400 journal publications.
Rao has received 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, the United Kingdom, the United States, and Italy. Rao was awarded the United States National Medal of Science, that nation's highest award for lifetime achievement in fields of scientific research, in June 2002. The latest addition to his collection of awards is the India Science Award for 2010, the highest honour conferred by the government of India in scientific domain. He has most recently been honoured with his 38th honorary doctorate by the Indian Institute of Technology, Kharagpur, on 26 July 2014 for "his contributions to the foundations of modern statistics through the introduction of concepts such as Cramér–Rao inequality, Rao–Blackwellization, Rao distance, Rao measure, and for introducing the idea of orthogonal arrays for the industry to design highquality products." (Rao's 37th honorary doctorate was given to him by the State University of New York at Buffalo at its 167th commencement in May 2013.)
He has been the President of the International Statistical Institute, Institute of Mathematical Statistics (USA), and the International Biometric Society. He was inducted into the Hall of Fame of India's National Institution for Quality and Reliability (Chennai Branch) for his contribution to industrial statistics and the promotion of quality control programs in industries.
The Journal of Quantitative Economics published a special issue in Rao's honour in 1991. "Dr Rao is a very distinguished scientist and a highly eminent statistician of our time. His contributions to statistical theory and applications are well known, and many of his results, which bear his name, are included in the curriculum of courses in statistics at bachelor's and master's level all over the world. He is an inspiring teacher and has guided the research work of numerous students in all areas of statistics. His early work had greatly influenced the course of statistical research during the last four decades. One of the purposes of this special issue is to recognize Dr Rao's own contributions to econometrics and acknowledge his major role in the development of econometric research in India."
Areas of research contributions
 Estimation theory
 Statistical inference and linear models
 Multivariate analysis
 Combinatorial design
 Orthogonal arrays
 Biometry
 Statistical genetics
 Generalized matrix inverses
 Functional equations
Awards and medals
 Sardar Patel Life time Achievement Award (Sardar Ratna) of the Sardar Patel Foundation India (2015)
 Guy Medal in Gold (2011) of the Royal Statistical Society^{[6]}
 India Science Award 2010 (the highest award in a scientific field presented by government of India)^{[7]}
 International Mahalanobis Prize (2003) of the International Statistical Institute^{[8]}
 Srinivasa Ramanujan Medal (2003) of the Indian National Science Academy
 President George W. Bush, on June 12, 2002, honoured him with the National Medal of Science, the highest award in U.S. in the scientific field, as a "prophet of new age" with the citation, "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."
 Padma Vibhushan (2001) by the Government of India^{[9]}
 Mahalanobis Centenary Gold Medal (1993?) of the Indian Science Congress
 Wilks Memorial Award (1989) of the American Statistical Association
 Padma Bhushan (1968)^{[9]}
 Megnadh Saha Medal (1969) of the Indian National Science Academy
 Guy Medal in Silver (1965) of the Royal Statistical Society
 S. S. Bhatnagar Award (1963) of Council of Scientific and Industrial Research
 JC Bose Gold Medal of the Bose Institute
 Gold Medal of the University of Calcutta
 He was also awarded an honorary Doctor of Science by the University of Calcutta in 2003.^{[10]} Also honorary doctorates from a number of universities and institutes around the world.
In his honor
 The Pennsylvania State University has established C. R. and Bhargavi Rao Prize in Statistics,
 CR Rao Advanced Institute of Mathematics, Statistics and Computer Science
 National Award in Statistics established by Ministry of Statistics and Programme Implementation (MoSPI), Government of India.
 The road from IIIT Hyderabad passing along Central University of Hyderabad crossroads to Alind Factory, Lingampally is named as "Prof. C.R. Rao Road".^{[11]}
Selected Publications
 2009. (with PEREIRA, B. de B.) Data Mining Using Neural Networks: A Guide for Statisticians. State College, Pennsylvania, 2009. 186 p.
 2006. (with B de Bragança Pereira).Data Mining Using Neural Networks: A Guide for Statisticians.
 1999. (with Helge Toutenburg, Andreas Fieger et al.). Linear Models: Least Squares and Alternatives, 2ed, Springer Series in Statistics. Springer
 1998. (with M. Bhaskara Rao). Matrix Algebra & Its Applications to Statistics & Econometrics. World Scientific
 1997. Statistics And Truth: Putting Chance To Work, 2ed. Wspc
 1996. Principal Component and Factor Analyses. PN
 1996. Extensions of a Characterization of an Exponential Distribution Based on a Censored Ordered Sample.
 1996. Bootstrap by Sequential Resampling. PN
 1993. Applications of Multivariate Analysis. PN
 1992. Signal Estimation, Multitarget Tracking and Related Areas.
 1989. Multivariate Analysis and Its Applications. PN
 1988. Linear Transformations, Projection Operators and Generalized Inverses; A Geometric Approach. PN
 1984. Recent Results on Characterization of Probability Distributions: A unified Approach through Extensions of Deny's Theorem. PN
 1973. Linear Statistical Inference and Its Applications, 2nd Edition. WileyInterscience
 1973. On a Unified Theory of Estimation in Linear Models. PN
 1973. (with A.M. Kagan et al.). Characterization Problems in Mathematical Statistics, Wiley Series in Probability & Mathematical Statistics.
 1972. (with Sujit Kumar Mitra). Generalized Inverse of Matrices and Its Applications, Probability & Mathematical Statistics. John Wiley & Sons
 1963. Essays on econometrics and planning. Statistical Pub. Society
 2015. (Ed. with Marepalli B. Rao). Handbook of Statistics 32: Computational Statistics with. Elsevier
 2013. (Ed. with Venu Govindaraju). Handbook of Statistics 31: Machine Learning: Theory and Applications. North Holland
 2012. (Ed. with Tata Subba Rao and Suhasini Subba Rao). Handbook of Statistics 30: Time Series Analysis: Methods and Applications . North Holland
 2009. (Ed. with Danny Pfeffermann). Handbook of Statistics 29A: Sample Surveys: Design, Methods and Applications. North Holland
 2009. (Ed. with Danny Pfeffermann). Handbook of statistics 29B Sample Surveys: Inference and Analysis. North Holland
 2012. (Ed. with Ranajit Chakraborty and Pranab K. Sen). Handbook of Statistics 28: Bioinformatics in Human Health and Heredity. North Holland
 2007. (Ed. with J. Philip Miller and D.C. Rao). Handbook of Statistics 27: Epidemiology and Medical Statistics. North Holland
 2006. (Ed. with Sandip Sinharay). Handbook of Statistics, Volume 26: Psychometrics. North Holland
 2005. (Ed. with Dipak K. Dey). Handbook of Statistics 25: Bayesian Thinking, Modeling and Computation. North Holland
 2005. (Ed.). Handbook of Statistics 24: Data Mining and Data Visualization. North Holland
 2004. (Ed. with N. Balakrishnan). Handbook of Statistics 23: Advances in Survival Analysis. North Holland
 2003. (Ed. with Ravindra Khattree). Handbook of Statistics 22: Statistics in Industry. North Holland
 2001. (Ed. with N. Balakrishnan). Handbook of Statistics 20: Advances in Reliability, NorthHolland Mathematics Studies. Elsevier
 2001. (Ed. with D. N. Shanbhag). Handbook of Statistics 19: Stochastic Processes: Theory and Methods. NorthHolland
 2000. (Ed. with Pranab Kumar Sen). Handbook of Statistics 18: Bioenvironmental and Public Health Statistics. NorthHolland
 1998. (Ed. with N. Balakrishnan). Handbook of Statistics 17: Order Statistics: Applications. NorthHolland
 1998. (Ed. with N. Balakrishnan). Handbook of Statistics 16: Order Statistics: Theory & Methods. NorthHolland
 1997. (Ed. with G.S. Maddala). Handbook of Statistics 15: Robust Inference. Elsevier
 1996. (Ed. with G.S. Maddala). Handbook of Statistics 14: Statistical Methods in Finance. Elsevier
 1996. (Ed. with S. Ghosh). Handbook of Statistics 13: Design and Analysis of Experiments. North Holland
 1994. (Ed. with G.P. Patil). Handbook of Statistics 12: Environmental Statistics. Elsevier
 1993. (Ed. with G. S. Maddala and H. D. Vinod). Handbook of Statistics 11: Econometrics, Techniques and Instrumentation in Analytical Chemistry. Elsevier
 1993. (Ed. with N. K. Bose). Handbook of Statistics 10: Signal Processing and its Applications, Elsevier
 1993. (Ed.). Handbook of Statistics 9: Computational Statistics. NorthHolland
 1991. (Ed. with R. Chakraborty). Handbook of Statistics 8: Statistical Methods in Biological and Medical Sciences. NorthHolland.
 1988. (Ed. with Krishnaiah P.R.). Handbook of Statistics 7: Quality Control and Reliability.
 1988. (Ed. with P. R. Krishnaiah). Handbook of Statistics 6: Sampling. NorthHolland.
 NOTE: Handbook of Statistics 15 were not edited by C. R. Rao, but by P. R. Krishnaiah.
 2011. (Ed. with Dipak K. Dey). Essential Bayesian Models. North Holland
 2011. (Ed. with Danny Pfeffermann). Essential Methods for Design Based Sample Surveys. North Holland
 1994. (Ed. with G.P. Patil). Multivariate Environmental Statistics., Volume 6 in NorthHolland Series in Statistics and Probability. North Holland
 1970. Advanced Statistical Methods in Biometric Research. Macmillan
 1969. (Ed. with R. C. Bose, I. M. Chakravarti et al.). Essays in Probability and Statistics, Monograph Series in Probability and Statistics. The University of North Carolina Press
 1995. Advances in Econometrics and Quantitative Economics, Essays in Honor of Professor C.R. Rao. (Eds.) G. S. Maddala, T. N. Srinivasan, and Peter C. B. Phillips. WileyBlackwell
 1982. Statistics and Probability: Essays in Honor of C. R. Rao. (Ed.). Kallinapur. Elsevier
 1996. Selected Papers of C.R. Rao 3. (Ed). S. Das Gupta et al. WileyInterscience
 1994. Selected Papers of C.R. Rao 1. (Ed). S. Das Gupta et al. WileyInterscience
See also
References
 ↑ "The Numberdars". The Times of India. 1 October 2011.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ ^{2.0} ^{2.1} ^{2.2} "Statisticians in History: Calyampudi R. Rao". American Statistical Association. horizontal tab character in
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tag; name "amstat" defined multiple times with different content  ↑ "C.R.Rao in News". C.R.Rao Advanced Institute of Mathematics, Statistics and Computer Science.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ "Indian Heart Association". Indian Heart Association Webpage. Retrieved 27 April 2015.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ "Profile". C.R.Rao Advanced Institute of Mathematics, Statistics and Computer Science.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ "Indian American C.R. Rao receives the RSS Guy Medal Award". Silicon India. 2 August 2011.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ "C.R. Rao Receives the India Science Award". Eberly College of Science, Penn State University. 19 October 2010.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ "The previous winners of the Award are Professor C.R. Rao (India) in 2003..." http://www.isiweb.org/component/content/article/43about/about/5882013mahalanobisinternationalawardinstatisticsannouncement
 ↑ ^{9.0} ^{9.1} "Padma Awards" (PDF). Ministry of Home Affairs, Government of India. 2015. Retrieved July 21, 2015.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ "Recipients of Honorary Degrees". University of Calcutta.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ "Road to be named after Prof. C.R. Rao". The Hindu. 10 September 2009. Retrieved 6 May 2012.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
Further reading
 Nalini Krishnankutty, 1996. Putting Chance to Work: A Life in Statistics: A Biography of C. R. Rao.
Sources
 Calyampudi Radhakrishnan Rao. University of Minnesota Morris
 Statisticians in History: Calyampudi R. Rao". American Statistical Association
 "Prof. C R Rao : An Eminent Statistician" By Bibhuprasad Mohapatra. Govt. of Odisha.
External links
 C. R. Rao Advanced Institute of Mathematics, India
 Prof. Rao's page at Penn State
 Prof. Rao's page at the University at Buffalo
 ET Interviews: Professor C. R. Rao on the Econometric Theory page.
 Royal Society citation 1967
 Rao was awarded the Samuel S. Wilks Award in 1989
 C.R. Rao at the Mathematics Genealogy Project
For the Cramér–Rao inequality and the Rao–Blackwell theorem see the relevant entries on
Photograph of Rao with Harald Cramér in 1978
 Pages with reference errors
 CS1 errors: invisible characters
 Articles with unsourced statements from December 2014
 Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science
 1920 births
 Living people
 20thcentury mathematicians
 Alumni of King's College, Cambridge
 American mathematicians
 Andhra University alumni
 Fellows of the American Statistical Association
 Fellows of the Royal Society
 Indian mathematicians
 Indian statisticians
 Telugu people
 Members of the United States National Academy of Sciences
 National Medal of Science laureates
 Pennsylvania State University faculty
 People from Bellary district
 Presidents of the Institute of Mathematical Statistics
 Presidents of the International Statistical Institute
 Recipients of the Padma Bhushan
 Recipients of the Padma Vibhushan
 University at Buffalo faculty
 University of Calcutta alumni
 Winners of the Guy Medal in Silver
 Winners of the Wilks Memorial Award
 Winners of the Guy Medal in Gold
 Indian Statistical Institute alumni
 Indian Statistical Institute faculty
 Andhra Pradesh scientists
 Karnataka scientists