C. R. Rao
Encyclopedia
Calyampudi Radhakrishna Rao FRS
known as C R Rao (born 10 September 1920) is an India
n statistician
. He is currently professor emeritus at Penn State University and Research Professor at the University at Buffalo. Rao has been honored by numerous colloquia, honorary degrees, and festschrift
s and was awarded the US National Medal of Science
in 2002. 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." The Times of India listed Rao as one of the top 10 Indian scientists of all time.
, India
. He received an MSc
degree in mathematics
from Andhra University
and an MSc degree in statistics
from Calcutta University in 1943.
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 Dr. 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 and the Rao–Blackwell theorem
both related to the quality of estimator
s. 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 over 34 honorary doctoral degrees from universities in 18 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 honor conferred by the government of India in scientific domain.
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.
For the Cramér–Rao inequality and the Rao–Blackwell theorem
see the relevant entries on
Photograph of Rao with Harald Cramér
in 1978
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
known as C R Rao (born 10 September 1920) is an India
India
India , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...
n statistician
Statistician
A statistician is someone who works with theoretical or applied statistics. The profession exists in both the private and public sectors. The core of that work is to measure, interpret, and describe the world and human activity patterns within it...
. He is currently professor emeritus at Penn State University and Research Professor at the University at Buffalo. Rao has been honored by numerous colloquia, honorary degrees, and festschrift
Festschrift
In academia, a Festschrift , is a book honoring a respected person, especially an academic, and presented during his or her lifetime. The term, borrowed from German, could be translated as celebration publication or celebratory writing...
s and was awarded the US National Medal of Science
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 sciences, biology, chemistry, engineering, mathematics and...
in 2002. The American Statistical Association
American Statistical Association
The American Statistical Association , is the main professional US organization for statisticians and related professions. It was founded in Boston, Massachusetts on November 27, 1839, and is the second oldest, continuously operating professional society in the United States...
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 listed Rao as one of the top 10 Indian scientists of all time.
Early life
C R Rao was born in Hadagali, KarnatakaKarnataka
Karnataka , the land of the Kannadigas, is a state in South West India. It was created on 1 November 1956, with the passing of the States Reorganisation Act and this day is annually celebrated as Karnataka Rajyotsava...
, India
India
India , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...
. He received an MSc
Master of Science
A Master of Science is a postgraduate academic master's degree awarded by universities in many countries. The degree is typically studied for in the sciences including the social sciences.-Brazil, Argentina and Uruguay:...
degree in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
from Andhra University
Andhra University
Andhra University or Andhra Viswa Kala Parishad , located in Visakhapatnam, north east coastal Andhra Pradesh, is one of the older premier universities in India with a broad focus...
and an MSc degree in statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
from Calcutta University in 1943.
Academic career
Rao worked at the Indian Statistical InstituteIndian Statistical Institute
Indian Statistical Institute is a public research institute and university in Kolkata's northern outskirt of Baranagar, India founded by Prasanta Chandra Mahalanobis in 1931...
and the Anthropological Museum in Cambridge
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
before acquiring a Ph.D.
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
degree at King's College
King's College, Cambridge
King's College is a constituent college of the University of Cambridge, England. The college's full name is "The King's College of our Lady and Saint Nicholas in Cambridge", but it is usually referred to simply as "King's" within the University....
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
University of Pittsburgh
The University of Pittsburgh, commonly referred to as Pitt, is a state-related research university located in Pittsburgh, Pennsylvania, United States. Founded as Pittsburgh Academy in 1787 on what was then the American frontier, Pitt is one of the oldest continuously chartered institutions of...
and Eberly Professor and Chair of Statistics and Director of the Center for Multivariate Analysis at the Pennsylvania State University
Pennsylvania State University
The Pennsylvania State University, commonly referred to as Penn State or PSU, is a public research university with campuses and facilities throughout the state of Pennsylvania, United States. Founded in 1855, the university has a threefold mission of teaching, research, and public service...
. 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 Dr. 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 and the Rao–Blackwell theorem
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-squared-error criterion or any of a variety of similar...
both related to the quality of estimator
Estimator
In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule and its result are distinguished....
s. Other areas he worked in include multivariate analysis
Multivariate analysis
Multivariate analysis is based on the statistical principle of multivariate statistics, which involves observation and analysis of more than one statistical variable at a time...
, estimation theory
Estimation theory
Estimation theory is a branch of statistics and signal processing that deals with estimating the values of parameters based on measured/empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the...
, 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 over 34 honorary doctoral degrees from universities in 18 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
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
, the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
, and Italy
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
. Rao was awarded the United States National Medal of Science
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 sciences, biology, chemistry, engineering, mathematics and...
, 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 honor conferred by the government of India in scientific domain.
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.
Areas of research contributions
- Estimation theoryEstimation theoryEstimation theory is a branch of statistics and signal processing that deals with estimating the values of parameters based on measured/empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the...
- Statistical inferenceStatistical inferenceIn statistics, statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation...
and linear modelLinear modelIn 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 is also used in time series analysis with a different...
s - Multivariate analysisMultivariate analysisMultivariate analysis is based on the statistical principle of multivariate statistics, which involves observation and analysis of more than one statistical variable at a time...
- Combinatorial designCombinatorial designCombinatorial design theory is the part of combinatorial mathematics that deals with the existence and construction of systems of finite sets whose intersections have specified numerical properties....
- Biometry
- Statistical genetics
- Generalized matrix inverseGeneralized inverseIn mathematics, a generalized inverse or pseudoinverse of a matrix A is a matrix that has some properties of the inverse matrix of A but not necessarily all of them...
s - Functional equations
Awards and medals
- Guy MedalGuy MedalThe Guy Medals are awarded by the Royal Statistical Society in three categories; Gold, Silver and Bronze. The Gold Medal is awarded triennially, the other two are awarded annually...
in Gold (2011) of the Royal Statistical SocietyRoyal Statistical SocietyThe Royal Statistical Society is a learned society for statistics and a professional body for statisticians in the UK.-History:It was founded in 1834 as the Statistical Society of London , though a perhaps unrelated London Statistical Society was in existence at least as early as 1824... - India Science Award 2010 (the highest award in a scientific field presented by government of India)http://sphhp.buffalo.edu/biostat/news_events/crrao.pdf
- International Mahalanobis Prize (2003) of the International Statistical InstituteInternational Statistical InstituteThe International Statistical Institute is a professional association of statisticians. The Institut International de Statistique or International Statistical Institute was founded in 1885 although there had been international congresses from 1853.. The Institute publishes a variety of books and...
- Srinivasa Ramanujan Medal (2003) of the Indian National Science AcademyIndian National Science AcademyThe Indian National Science Academy , New Delhi is the apex body of Indian scientists representing all branches of science & technology.-History:...
- President George W. BushGeorge W. BushGeorge Walker Bush is an American politician who served as the 43rd President of the United States, from 2001 to 2009. Before that, he was the 46th Governor of Texas, having served from 1995 to 2000....
, on June 12, 2002, honored him with the National Medal of ScienceNational Medal of ScienceThe 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 sciences, biology, chemistry, engineering, mathematics and...
, 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 VibhushanPadma VibhushanThe Padma Vibhushan is the second highest civilian award in the Republic of India. It consists of a medal and a citation and is awarded by the President of India. It was established on 2 January 1954. It ranks behind the Bharat Ratna and comes before the Padma Bhushan...
(2001) by the Government of IndiaGovernment of IndiaThe Government of India, officially known as the Union Government, and also known as the Central Government, was established by the Constitution of India, and is the governing authority of the union of 28 states and seven union territories, collectively called the Republic of India... - Mahalanobis Centenary Gold Medal (1993?) of the Indian Science Congress
- Wilks Memorial AwardWilks Memorial AwardThe Wilks Memorial Award is awarded by the American Statistical Association to recognize outstanding contributions to statistics. It was established in 1964 and is awarded yearly. It is named in memory of the statistician Samuel S. Wilks. The award consists of a medal, a citation and a cash...
(1989) of the American Statistical AssociationAmerican Statistical AssociationThe American Statistical Association , is the main professional US organization for statisticians and related professions. It was founded in Boston, Massachusetts on November 27, 1839, and is the second oldest, continuously operating professional society in the United States... - Megnadh Saha Medal (1969) of the Indian National Science Academy
- Guy MedalGuy MedalThe Guy Medals are awarded by the Royal Statistical Society in three categories; Gold, Silver and Bronze. The Gold Medal is awarded triennially, the other two are awarded annually...
in Silver (1965) of the Royal Statistical SocietyRoyal Statistical SocietyThe Royal Statistical Society is a learned society for statistics and a professional body for statisticians in the UK.-History:It was founded in 1834 as the Statistical Society of London , though a perhaps unrelated London Statistical Society was in existence at least as early as 1824... - S. S. Bhatnagar Award (1963) of Council of Scientific and Industrial Research
- JC Bose Gold Medal of the Bose InstituteBose InstituteBose Institute is a research institute in the fields of Physics, Chemistry, Plant biology, Microbiology, Biochemistry, Biophysics, Animal physiology, Immunotechnology and Environmental science. The institute was established in 1917 by Acharya Jagdish Chandra Bose, who was the founder of modern...
- Gold Medal of the University of CalcuttaUniversity of CalcuttaThe University of Calcutta is a public university located in the city of Kolkata , India, founded on 24 January 1857...
- He was also awarded an honorary Doctor of ScienceDoctor of ScienceDoctor of Science , usually abbreviated Sc.D., D.Sc., S.D. or Dr.Sc., is an academic research degree awarded in a number of countries throughout the world. In some countries Doctor of Science is the name used for the standard doctorate in the sciences, elsewhere the Sc.D...
by the University of CalcuttaUniversity of CalcuttaThe University of Calcutta is a public university located in the city of Kolkata , India, founded on 24 January 1857...
in 2003. Also honorary doctorates from a number of universities and institutes around the world.
In his honor
- The Pennsylvania State UniversityPennsylvania State UniversityThe Pennsylvania State University, commonly referred to as Penn State or PSU, is a public research university with campuses and facilities throughout the state of Pennsylvania, United States. Founded in 1855, the university has a threefold mission of teaching, research, and public service...
has established C. R. and Bhargavi Rao Prize in statistics, - CR Rao Advanced Institute of Mathematics, Statistics and Computer ScienceCR Rao Advanced Institute of Mathematics, Statistics and Computer ScienceCR Rao Advanced Institute of Mathematics, Statistics and Computer Science was founded in 2007 as a leading institute for basic research in statistics, computer science and mathematics. It is located on the campus of the University of Hyderabad and construction is underway.It is named after CR Rao,...
- National Award in Statistics established by Ministry of Statistics and Programme Implementation (MoSPI), Government of India.
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
For the Cramér–Rao inequality and the Rao–Blackwell theorem
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-squared-error criterion or any of a variety of similar...
see the relevant entries on
Photograph of Rao with Harald Cramér
Harald Cramér
Harald Cramér was a Swedish mathematician, actuary, and statistician, specializing in mathematical statistics and probabilistic number theory. He was once described by John Kingman as "one of the giants of statistical theory".-Early life:Harald Cramér was born in Stockholm, Sweden on September...
in 1978
