CR Rao wins top statistics award – looking back at his pioneering work

Indian-American statistician Kalyampudi Radhakrishna Rao has been awarded the 2023 International Prize in Statistics, which is the statistical equivalent of the Nobel Prize. This was established in 2016 and is awarded every two years to an individual or team “for major achievements using statistics to advance science, technology and human interest.”

Prof. Rao, who is now 102 years old, is a “living legend” whose work, in the words of the American Statistical Association, was “not only statistical” but also “economics, genetics, anthropology, geology, national policy”; demography, biometrics and medicine”. The quote for the new award reads: “CR Rao, a professor whose work over 75 years continues to exert a profound influence on science, has been awarded the 2023 International Prize in Statistics.”

What is Rao’s 1945 paper about?

Rao’s seminal paper, ‘Information and accuracy in statistical parameter estimation’, was published in 1945. Bulletin of the Calcutta Mathematical Society, a journal otherwise known to the statistical community. The paper was later included in the book Breakthroughs in Statistics, 1890-1990.

This was an impressive achievement given that Rao was only 25 at the time and had just completed his master’s degree in statistics two years earlier.

He did his PhD in 1946-1948 at the University of Cambridge at King’s College, under the supervision of Ronald A. Fisher, widely regarded as the father of modern textbooks.

The Cramér-Rao inequality is the first of the three results of the 1945 paper. When we estimate the value of an unknown module, we need to know the margin of error of the estimator. Rao’s work provided a lower bound for the estimation of weighted odds for a finite sample. This is so, because in mathematics statistics has become a cornerstone; Researchers have highlighted it as multifarious, with applications also in quantum physics, signal processing, spectroscopy, radar systems, complex radiography imaging, risk analysis, and probability theory, among others.

in an * published articles in the newspaper Statistical Science In 1987, the American statistician Morris H. DeGroot solved the problem of the range (corroborated by Rao’s own method) of Rao’s method to reach the lower bound. Fisher had already established an asymptotic (ie, with the largest sample size) version of the inequality, and it seems that the student asked Rao, “Why don’t you try finite samples?” In 1944. A then 24 year old Rao did this in less than 24 hours!

The second result of the 1945 paper was the Rao-Blackwell Theorem, which provides a method for improving the estimate when an the best to appreciate The Rao-Blackwell theorem and the Cramér-Rao inequality both relate to the quality of estimators.

A new interdisciplinary field called ‘information geometry’ was born from the third discovery of papers. This field integrated principles from differential geometry into statistics, including metric concepts, distances, and measurements. Erich L. Lehmann, the famous statistician, said in 2008 that “this work” [of Rao’s] He was ahead of his time and only came into his own in the 1980s”.

Thus, overall, Rao’s 1945 paper contributed brilliantly to the development of modern statistics and its widespread use in modern research. In the book of 2008, Reminiscence of a Statistician: The Company I KeptLehmann also acknowledged the generative nature of the paper – namely the gold insight that it was – that “most of the early papers arose from Rao’s paper of 1945”.

How did Rao change the field?

Australian statistician Terry Speed ​​asserted that “the 1940s cr Rao was sluggish. His 1945 paper … will prove that he did nothing else, but much else.

In fact, one of Rao’s papers in 1948 proposed a new generic approach to testing hypotheses, now popularized as the “Rao score test”. In fact, three types of tests – the probability test of Jerzy Neyman and ES Pearson (1928), the Wald test (1943) of Abraham Wald and the Rao score test (1948) – are sometimes called the “holy trinity”. about this kind of books.

Rao also contributed to orthogonal dressings, a concept in combinatorics that was used to design experiments, the results of which are qualitatively good, as early as 1949. From 1969 Forbes The article described it as the “new mantra” in industrial establishments.

Given the magnitude and relevance of his contributions, it might seem surprising that Rao entered the field of statistics by accident.

Although he first majored in mathematics at Andhra University, Rao obtained a 19-year scholarship there for administrative purposes. He was also rejected for the job of mathematician in the army’s survey unit, because he was judged to be underage.

While staying in a hotel in Calcutta, he met a man who was visiting Bombay and was sent to Calcutta to train at the Indian Statistical Institute. Rao requested that the institute also apply. Rao did so, after years of training in statistics, hoping the added qualification would help the job.

PC Mahalanobis, then director of the institute, responded promptly and Rao was enrolled. That marked the beginning of the institution’s four-decade stay. Rao retired in 1979 and later in the US

The first part of the 20th century was the golden period of statistical theory in general, and Rao is undoubtedly one of the reasons for this, due to his mathematical genius. In the words of the late mathematician Samuel Karlin, Rao’s contributions to statistical theory “earned him a place in the history books.”

The Indian statistician Prof. Rao should be thanked for his immense contributions to the growth of statistics in the country, notably at the Indian Statistical Institute (where this author works). As Lehmann wrote, Rao was “the person who carried on much of Mahalanobis’s work as chief statistician in India”.

Atanu Biswas is Professor of Statistics, Indian Statistical Institute, Kolkata.

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