Calyampudi Radhakrishna Rao FRS (born 10 September 1920), commonly known as C. R. Rao, is an

Indian-American Indian Americans or Indo-Americans are citizens of the United States with ancestry from India. The United States Census Bureau uses the term Asian Indian to avoid confusion with Native Americans, who have also historically been referred to ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

and statistician. He is currently

professor emeritus ''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title ...

at Pennsylvania State University and Research Professor at the

University at Buffalo The State University of New York at Buffalo, commonly called the University at Buffalo (UB) and sometimes called SUNY Buffalo, is a public research university with campuses in Buffalo and Amherst, New York. The university was founded in 18 ...

. Rao has been honoured by numerous colloquia, honorary degrees, and

festschrift In academia, a ''Festschrift'' (; plural, ''Festschriften'' ) is a book honoring a respected person, especially an academic, and presented during their lifetime. It generally takes the form of an edited volume, containing contributions from the h ...

s and was awarded the US

National Medal of Science The National Medal of Science is an honor bestowed by the President of the United States to individuals in science and engineering who have made important contributions to the advancement of knowledge in the fields of behavioral and social scienc ...

in 2002. The

American Statistical Association The American Statistical Association (ASA) is the main professional organization for statisticians and related professionals in the United States. It was founded in Boston, Massachusetts on November 27, 1839, and is the second oldest continuousl ...

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." ''

The Times of India ''The Times of India'', also known by its abbreviation ''TOI'', is an Indian English-language daily newspaper and digital news media owned and managed by The Times Group. It is the third-largest newspaper in India by circulation and largest ...

'' listed Rao as one of the top 10 Indian scientists of all time. Rao is also a Senior Policy and Statistics advisor for the Indian Heart Association non-profit focused on raising South Asian cardiovascular disease awareness.

Early life

C. R. Rao was the eighth of the ten children born to a Telugu family in

Hadagali Huvina Hadagali is a town in Vijayanagara district. Historical names of Huvina Hadagali *Puvina-Posavadangile : An inscription found on a slab set up at the western entrance into the Keshavaswami temple at Huvina Hadagali, records that "Rebbal ...

Bellary Bellary, officially Ballari, in the eponymous Bellary district, is a city in the state of Karnataka, India. History Bellary was a part of Rayalaseema (Ceded Districts) which was part of Madras Presidency till 1 November 1956. The Ballari ...

, Madras Presidency (now in

Karnataka Karnataka (; ISO: , , also known as Karunāḍu) is a state in the southwestern region of India. It was formed on 1 November 1956, with the passage of the States Reorganisation Act. Originally known as Mysore State , it was renamed ''Karnat ...

), India. His schooling was completed in Gudur,

Nuzvid Nuzvid is a city in Eluru district of the Indian state of Andhra Pradesh. It serves as the administrative headquarters for Nuzvid mandal and Nuzvid revenue division. Geography Nuzvid is located at . It has an average elevation of . Demogra ...

Nandigama Nandigama is a town in NTR district of the Indian state of Andhra Pradesh. It is a Municipality and also the headquarters of Nandigama mandal in Nandigama revenue division. Geography Nandigama is located 50 km West of Vijayawada and 46&n ...

, and

Visakhapatnam , image_alt = , image_caption = From top, left to right: Visakhapatnam aerial view, Vizag seaport, Simhachalam Temple, Aerial view of Rushikonda Beach, Beach road, Novotel Visakhapatnam, INS Kursura submarine museu ...

, all in the present state of

Andhra Pradesh Andhra Pradesh (, abbr. AP) is a state in the south-eastern coastal region of India. It is the seventh-largest state by area covering an area of and tenth-most populous state with 49,386,799 inhabitants. It is bordered by Telangana to the ...

. He received an MSc in mathematics from

Andhra University Andhra University ( IAST: ''Āndhra Vișvakalāpariṣhat'') is a public university located in Visakhapatnam, Andhra Pradesh, India. It was established in 1926. History King Vikram Deo Verma, the Maharaja of Jeypore was one of the biggest d ...

and an MA in statistics from

Calcutta University The University of Calcutta (informally known as Calcutta University; CU) is a Public university, public collegiate university, collegiate State university (India), state university in India, located in Kolkata, West Bengal, India. Considered ...

in 1943. He obtained a PhD degree at King's College in

Cambridge University The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209 and granted a royal charter by Henry III of England, Henry III in 1231, Cambridge is the world' ...

under R. A. Fisher in 1948, to which he added a DSc degree, also from Cambridge, in 1965. Rao first worked at the

Indian Statistical Institute Indian Statistical Institute (ISI) is a higher education and research institute which is recognized as an Institute of National Importance by the 1959 act of the Indian parliament. It grew out of the Statistical Laboratory set up by Prasanta ...

and the Anthropological Museum in

Cambridge Cambridge ( ) is a College town, university city and the county town in Cambridgeshire, England. It is located on the River Cam approximately north of London. As of the 2021 United Kingdom census, the population of Cambridge was 145,700. Cam ...

. Later 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 The University of Pittsburgh (Pitt) is a public state-related research university in Pittsburgh, Pennsylvania. The university is composed of 17 undergraduate and graduate schools and colleges at its urban Pittsburgh campus, home to the univers ...

and Eberly Professor and Chair of Statistics and Director of the Center for Multivariate Analysis at 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. Among his best-known discoveries are the

Cramér–Rao bound In estimation theory and statistics, the Cramér–Rao bound (CRB) expresses a lower bound on the variance of unbiased estimators of a deterministic (fixed, though unknown) parameter, the variance of any such estimator is at least as high as the ...

and the

Rao–Blackwell theorem In statistics, the Rao–Blackwell theorem, sometimes referred to as the Rao–Blackwell–Kolmogorov theorem, is a result which characterizes the transformation of an arbitrarily crude estimator into an estimator that is optimal by the mean-squ ...

both related to the quality of

estimator In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. For example, the ...

s. Other areas he worked in include

multivariate analysis Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable. Multivariate statistics concerns understanding the different aims and background of each of the dif ...

, 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

, that nation's highest award for lifetime achievement in fields of scientific research, in June 2002. He was given the India Science Award in 2010, the highest honor conferred by the government of India in a scientific domain. In 2013, he was nominated for the Nobel Peace Prize, along with Miodrag Lovric (Editor) and Shlomo Sawilowsky, for their contribution to the

International Encyclopedia of Statistical Science The ''International Encyclopedia of Statistical Science'' is a statistical sciences reference published by Springer. It has been described as one of the scientific projects with the largest number of involved countries ever, since it includes contr ...

. He was most recently 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 high-quality products." He was 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 honor 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 model In statistics, the term linear model is used in different ways according to the context. The most common occurrence is in connection with regression models and the term is often taken as synonymous with linear regression model. However, the term ...

s *

Multivariate analysis Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable. Multivariate statistics concerns understanding the different aims and background of each of the dif ...

Combinatorial design Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of ''balance'' and/or ''symmetry''. These co ...

* Orthogonal arrays *

Biometry Biostatistics (also known as biometry) are the development and application of statistical methods to a wide range of topics in biology. It encompasses the design of biological experiments, the collection and analysis of data from those experimen ...

* Statistical genetics * Generalized matrix inverses *

Functional equations In mathematics, a functional equation is, in the broadest meaning, an equation in which one or several functions appear as unknowns. So, differential equations and integral equations are functional equations. However, a more restricted meaning ...

Awards and medals

* Guy Medal in Gold (2011) of the

Royal Statistical Society The Royal Statistical Society (RSS) is an established statistical society. It has three main roles: a British learned society for statistics, a professional body for statisticians and a charity which promotes statistics for the public good. ...

* India Science Award 2010 (the highest award in a scientific field presented by government of India) * International Mahalanobis Prize (2003) of the International Statistical Institute * Srinivasa Ramanujan Medal (2003) of the

Indian National Science Academy The Indian National Science Academy (INSA) is a national academy in New Delhi for Indian scientists in all branches of science and technology. In August 2019, Dr. Chandrima Shaha was appointed as the president of Indian National Science Acade ...

Sardar Patel Vallabhbhai Jhaverbhai Patel (; ; 31 October 1875 – 15 December 1950), commonly known as Sardar, was an Indian lawyer, influential political leader, barrister and statesman who served as the first Deputy Prime Minister and Home Minister of I ...

Lifetime Achievement International Award (Sardar Ratna) (2014) by Sardar Patel International Foundation,

India India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the so ...

* President George W. Bush, on 12 June 2002, honoured him with the

, the highest award in US 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 The Padma Vibhushan ("Lotus Decoration") is the second-highest civilian award of the Republic of India, after the Bharat Ratna. Instituted on 2 January 1954, the award is given for "exceptional and distinguished service". All persons without ...

(2001) by the

Government of India The Government of India (ISO: ; often abbreviated as GoI), known as the Union Government or Central Government but often simply as the Centre, is the national government of the Republic of India, a federal democracy located in South Asia, ...

* Mahalanobis Centenary Gold Medal (1993?) of the

Indian Science Congress Indian Science Congress Association(ISCA) is a premier scientific organisation of India with headquarters at Kolkata, West Bengal. The association started in the year 1914 in Kolkata and it meets annually in the first week of January. It has a ...

* Wilks Memorial Award (1989) of the

Padma Bhushan The Padma Bhushan is the third-highest civilian award in the Republic of India, preceded by the Bharat Ratna and the Padma Vibhushan and followed by the Padma Shri. Instituted on 2 January 1954, the award is given for "distinguished service ...

(1968) * Megnadh Saha Medal (1969) of the Indian National Science Academy * Guy Medal in Silver (1965) of the

* S. S. Bhatnagar Award (1963) of

Council of Scientific and Industrial Research The Council of Scientific and Industrial Research ( IAST: ''vaigyanik tathā audyogik anusandhāna pariṣada''), abbreviated as CSIR, was established by the Government of India in September 1942 as an autonomous body that has emerged as the ...

* JC Bose Gold Medal of the Bose Institute * Gold Medal of the

University of Calcutta The University of Calcutta (informally known as Calcutta University; CU) is a public collegiate state university in India, located in Kolkata, West Bengal, India. Considered one of best state research university all over India every year, ...

* He was also awarded an honorary

Doctor of Science Doctor of Science ( la, links=no, Scientiae Doctor), usually abbreviated Sc.D., D.Sc., S.D., or D.S., is an academic research degree awarded in a number of countries throughout the world. In some countries, "Doctor of Science" is the degree used f ...

by the

in 2003. Also honorary doctorates from a number of universities and institutes around the world.

In his honour

* The Pennsylvania State University has established C. R. and Bhargavi Rao Prize in Statistics *

CR Rao Advanced Institute of Mathematics, Statistics and Computer Science CR Rao Advanced Institute of Mathematics, Statistics and Computer Science (also called AIMSCS) was founded in 2007 as an institute for basic research in statistics, computer science and mathematics. It is located on the campus of the University of ...

* National Award in Statistics established by

Ministry of Statistics and Programme Implementation The Ministry of Statistics and Programme Implementation (MoSPI) is a ministry of Government of India concerned with coverage and quality aspects of statistics released. The surveys conducted by the Ministry are based on scientific sampling metho ...

(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".

Selected publications

Books * 2020. PEREIRA, B. de B.; RAO, Calyampudi Radhakrishna.; OLIVEIRA, F. B.;Statistical Learning Using Neural Networks: A Guide for Statisticians and Data Scientists with Python, CRC Press, London. * 2017
Book Review: Multivariate Statistical Methods, A Primer
* 2016. (with Lovric, M.
Testing Point Null Hypothesis of a Normal Mean and the Truth: 21st Century Perspective
* 2009. (with PEREIRA, B. de B.) Data Mining Using Neural Networks: A Guide for Statisticians. State College, Pennsylvania, 2009. 186 p. * 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. Wiley-Interscience * 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 Edited Volumes * 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 * 2012. (Ed. with Ranajit Chakraborty and Pranab K. Sen). ''Handbook of Statistics 28: Bioinformatics in Human Health and Heredity''. North Holland * 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 * 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 * 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'', North-Holland Mathematics Studies. Elsevier * 2001. (Ed. with D. N. Shanbhag). ''Handbook of Statistics 19: Stochastic Processes: Theory and Methods''. North-Holland * 2000. (Ed. with Pranab Kumar Sen). ''Handbook of Statistics 18: Bioenvironmental and Public Health Statistics''. North-Holland * 1998. (Ed. with N. Balakrishnan). ''Handbook of Statistics 17: Order Statistics: Applications''. North-Holland * 1998. (Ed. with N. Balakrishnan). ''Handbook of Statistics 16: Order Statistics: Theory & Methods''. North-Holland * 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 * 1994. (Ed. with G.P. Patil). ''Multivariate Environmental Statistics.'', Volume 6 in North-Holland Series in Statistics and Probability. North Holland * 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''. North-Holland * 1991. (Ed. with R. Chakraborty). ''Handbook of Statistics 8: Statistical Methods in Biological and Medical Sciences''. North-Holland. * 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''. North-Holland. * 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 Textbooks * 1970. ''Advanced Statistical Methods in Biometric Research''. Macmillan Collected Works * 1996. ''Selected Papers of C.R. Rao 3''. (Ed). S. Das Gupta et al. Wiley-Interscience * 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. Wiley-Blackwell * 1994. ''Selected Papers of C.R. Rao 2''. (Ed). S. Das Gupta et al. Wiley-Interscience * 1994. ''Selected Papers of C.R. Rao 1''. (Ed). S. Das Gupta et al. Wiley-Interscience * 1982. ''Statistics and Probability: Essays in Honor of C. R. Rao''. (Ed.). Kallinapur. Elsevier

References

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

Prof. Rao's page at Penn State

Prof. Rao's page at the University at Buffalo

ET Interviews: Professor C. R. Rao
on th
Econometric Theory
page.
Royal Society citation 1967

Rao was awarded the Samuel S. Wilks Award in 1989
* * For the Cramér–Rao inequality and the

see the relevant entries on
Earliest Known Uses of Some of the Words of Mathematics
For Rao contribution to information geometry
Cramer-Rao Lower Bound and Information Geometry
Photograph of Rao with Harald Cramér in 1978
C. R. Rao
from th

{{DEFAULTSORT:Rao, C. R. 1920 births Living people 20th-century Indian mathematicians Alumni of King's College, Cambridge 20th-century American mathematicians Andhra University alumni Fellows of the American Statistical Association Fellows of the Royal Society 21st-century Indian mathematicians Indian statisticians Telugu people Members of the United States National Academy of Sciences National Medal of Science laureates Pennsylvania State University faculty American people of Telugu descent People from Bellary district Presidents of the Institute of Mathematical Statistics Presidents of the International Statistical Institute Recipients of the Padma Bhushan in science & engineering Recipients of the Padma Vibhushan in science & engineering University at Buffalo faculty University of Calcutta alumni Indian Statistical Institute alumni Indian Statistical Institute faculty Scientists from Andhra Pradesh American academics of Indian descent Fellows of the Econometric Society Recipients of the Shanti Swarup Bhatnagar Award in Mathematical Science American centenarians Indian centenarians Men centenarians People from Andhra Pradesh Probability theorists Detection and estimation theorists 21st-century American mathematicians Indian emigrants to the United States American expatriates in the United Kingdom American people of Indian descent