C. R. Rao

Calyampudi Radhakrishna Rao
Born	September 10, 1920 Hadagali, Karnataka, India
Residence	India , UK , USA
Nationality	Indian- American
Field	Mathematician
Institutions	Indian Statistical Institute Cambridge University Penn State University
Alma mater	Andhra University Calcutta University Cambridge University
Academic advisor	Ronald Fisher
Notable students	Debabrata Basu S. R. S. Varadhan Ranajit Chakraborty[1] K. R. Parthasarathy
Known for	Cramér-Rao bound Rao-Blackwell theorem
Notable prizes	Mahalanobis medal, Padma Vibhushan National Medal of Science

Calyampudi Radhakrishna Rao (born September 10, 1920) is a famous Indian statistician and currently professor emeritus at Penn State University. He was born in Hadagali, Karnataka state, India. Image File history File links No higher resolution available. ... is the 253rd day of the year (254th in leap years) in the Gregorian calendar. ... 1920 (MCMXX) was a leap year starting on Thursday. ... Karnātakā   (Kannada: ಕನಾ೯ಟಕ) (IPA: ) is one of the four southern states of India. ... Image File history File links Flag_of_India. ... Image File history File links Flag_of_the_United_Kingdom. ... Image File history File links This is a lossless scalable vector image. ... Image File history File links Flag_of_India. ... Image File history File links This is a lossless scalable vector image. ... Leonhard Euler, one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... Indian Statistical Institute (ISI), is a unique institution devoted to the research, teaching and application of statistics, natural sciences and social sciences. ... The University of Cambridge is the second-oldest university in the English-speaking world, with one of the most selective sets of entry requirements in the United Kingdom. ... The Pennsylvania State University The Pennsylvania State University (commonly known as Penn State) is a state-related land-grant university in Pennsylvania, with over 80,000 students at 24 campuses throughout the state. ... Andhra University, located in Visakhapatnam, is one of the older premier universities in India with a broad focus. ... Established in January 24, 1857, the University of Calcutta (also known as Calcutta University) is the first modern university in the Indian sub_continent. ... Sir Ronald Aylmer Fisher, FRS (17 February 1890 – 29 July 1962) was a British statistician, evolutionary biologist, and geneticist. ... Debabrata Basu (1925 - March 24, 2001) Indian statistician, who specialised in the foundations of statistics. ... Sathamangalam R. Srinivasa Varadhan is an Indian-American probabilist. ... Professor Ranajit Chakraborty is a famous human geneticist and currently the Robert A. Kehoe Professor and Director of Center for Genome Information at College of Medicine, University of Cincinnati. ... In statistics, the Cramér-Rao bound (CRB) or Cramér-Rao lower bound (CRLB), named in honor of Harald Cramér and Calyampudi Radhakrishna Rao, expresses a lower bound on the variance of estimators of a deterministic parameter. ... In statistics, the Rao-Blackwell theorem describes a technique that can transform an absurdly crude estimator into an estimator that is optimal by the mean-squared-error criterion or any of a variety of similar criteria. ... National Medal of Science The National Medal of Science, also called the Presidential Medal of Science, is an honor given 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... is the 253rd day of the year (254th in leap years) in the Gregorian calendar. ... 1920 (MCMXX) was a leap year starting on Thursday. ... Statisticians are mathematicians who work with theoretical and applied statistics in the both the private and public sectors. ... The Pennsylvania State University The Pennsylvania State University (commonly known as Penn State) is a state-related land-grant university in Pennsylvania, with over 80,000 students at 24 campuses throughout the state. ... Karnātakā   (Kannada: ಕನಾ೯ಟಕ) (IPA: ) is one of the four southern states of India. ...

He received an M.S. in mathematics from Andhra University and an M.S. in Statistics from Calcutta University in 1943. A masters degree is an academic degree usually awarded for completion of a postgraduate course of one or two years in duration. ... Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... Andhra University, located in Visakhapatnam, is one of the older premier universities in India with a broad focus. ... A graph of a normal bell curve showing statistics used in educational assessment and comparing various grading methods. ... Established in January 24, 1857, the University of Calcutta (also known as Calcutta University) is the first modern university in the Indian sub_continent. ... Year 1943 (MCMXLIII) was a common year starting on Friday (the link will display full 1943 calendar) of the Gregorian calendar. ...

Rao worked at the Indian Statistical Institute and the Anthropological Museum in Cambridge before acquiring a Ph.D. at King's College in Cambridge University under R.A. Fisher in 1948, to which he added a Sc.D. also from Cambridge in 1965. Indian Statistical Institute (ISI), is a unique institution devoted to the research, teaching and application of statistics, natural sciences and social sciences. ... The University of Cambridge (often Cambridge University), located in Cambridge, England, is the second-oldest university in the English-speaking world and has a reputation as one of the worlds most prestigious universities. ... Doctor of Philosophy (Ph. ... Full name The King’s College of Our Lady and St Nicholas in Cambridge Motto Veritas et Utilitas Truth and usefulness Named after Henry VI Previous names - Established 1441 Sister College(s) New College, Oxford Provost Prof. ... The University of Cambridge is the second-oldest university in the English-speaking world, with one of the most selective sets of entry requirements in the United Kingdom. ... Sir Ronald Fisher Sir Ronald Aylmer Fisher, FRS (February 17, 1890–July 29, 1962) was an extraordinarily talented evolutionary biologist, geneticist and statistician. ... 1948 (MCMXLVIII) was a leap year starting on Thursday (the link is to a full 1948 calendar). ... Sc. ... Year 1965 (MCMLXV) was a common year starting on Friday (link will display full calendar) of the 1965 Gregorian calendar. ...

Among his best known 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 and differential geometry. In statistics, the Cramér-Rao bound (CRB) or Cramér-Rao lower bound (CRLB), named in honor of Harald Cramér and Calyampudi Radhakrishna Rao, expresses a lower bound on the variance of estimators of a deterministic parameter. ... In statistics, the Rao-Blackwell theorem describes a technique that can transform an absurdly crude estimator into an estimator that is optimal by the mean-squared-error criterion or any of a variety of similar criteria. ... In statistics, an estimator is a function of the observable sample data that is used to estimate an unknown population parameter; an estimate is the result from the actual application of the function to a particular set of data. ... In statistics, in multivariate data, each data point has more than one scalar component, and often one is concerned with correlations between the components. ... Analysis has its beginnings in the rigorous formulation of calculus. ... In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ...

Dr. Rao is a Wilks and Mahalanobis medalist; a member of eight National Academies in India, the United Kingdom, the United States, and Italy; he has received dozens of medals, citations, awards, and other honors for his contributions to statistics and science. Dr. 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. National Medal of Science The National Medal of Science, also called the Presidential Medal of Science, is an honor given 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... For album titles with the same name, see 2002 (album). ...

Areas of research contributions of Professor Rao include

• Estimation theory
• Inference and linear models
• Multivariate analysis
• Combinatorial design
• Biometry
• Mathematical genetics
• Generalized matrix inverses
• Functional equations

Awards & Medals: Estimation theory is a branch of statistics and signal processing that deals with estimating the values of parameters based on measured/empirical data. ... In statistics the linear model can be expressed by saying where Y is an n×1 column vector of random variables, X is an n×p matrix of known (i. ... Multivariate statistics or multivariate statistical analysis in statistics describes a collection of procedures which involve observation and analysis of more than one statistical variable at a time. ... Combinatorial 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. ... This page is a candidate to be moved to Wiktionary. ... In mathematics or its applications, a functional equation is an equation in terms of independent variables, and also unknown functions, which are to be solved for. ...

• Government of India awarded him Padma Vibhushan.
• President Bush, on June 12,2002, decorated him with ‘NationalMedal of Science’
• Wilks Medal of the American Statistical Association,
• Guy Medal in Silver of the Royal Statistical Society,
• Megnadh Saha Medalof the Indian National Science Academy,
• S. S. Bhatnagar Award
• JC Bose Gold Medal of Bose Institute, and
• Mahalanobis Centenary Gold Medal of the Indian Science Congress.

In his honor,

• The Pennsylvania State University has established C. R. and Bhargavi Rao Prize in statistics,
• Osmania University has founded C.R. Rao Advanced Institute for Mathematical and Computer Sciences (AIMCS).

See also

• Cramér-Rao bound

In statistics, the Cramér-Rao bound (CRB) or Cramér-Rao lower bound (CRLB), named in honor of Harald Cramér and Calyampudi Radhakrishna Rao, expresses a lower bound on the variance of estimators of a deterministic parameter. ...

References

• UMN
• Amstat
• M. H. DeGroot A Conversation with C.R. Rao, Statistical Science, 2 (1987), 53-67.

External links

• Prof. Rao's page at Penn State

• 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 Rao’s PhD students see

• Mathematics Genealogy Project

For the Cramér-Rao inequality and the Rao-Blackwell theorem see the relevant entries on

• Earliest Known Uses of Some of the Words of Mathematics

Photograph of Rao with Harald Cramér in 1978 Harald Cramér (September 25, 1893 - October 5, 1985) was a Swedish mathematician and statistician, specialised in mathematical statistics. ...

• C. R. Rao from the PORTRAITS OF STATISTICIANS