The Indian-American statistician Calyampudi Radhakrishna Rao has been awarded the 2023 International Prize in Statistics, which is statistics’ equal of the Nobel Prize. It was established in 2016 and is awarded as soon as each two years to a person or workforce “for major achievements using statistics to advance science, technology and human welfare.”
Prof. Rao, who’s now 102 years previous, is a ‘living legend’ whose work has influenced, within the phrases of the American Statistical Association, “not just statistics” but additionally “economics, genetics, anthropology, geology, national planning, demography, biometry, and medicine”. The quotation for his new award reads: “C.R. Rao, a professor whose work more than 75 years ago continues to exert a profound influence on science, has been awarded the 2023 International Prize in Statistics.”
What was Rao’s 1945 paper about?
Rao’s groundbreaking paper, ‘Information and accuracy attainable in the estimation of statistical parameters’, was revealed in 1945 within the Bulletin of the Calcutta Mathematical Society, a journal that’s in any other case not well-known to the statistics group. The paper was subsequently included within the guide Breakthroughs in Statistics, 1890-1990.
This was a formidable achievement given Rao was solely 25 at the time and had simply accomplished his grasp’s diploma in statistics two years prior.
He would go on to do his PhD in 1946-1948 at King’s College, Cambridge University, below the supervision of Ronald A. Fisher, extensively considered the daddy of contemporary statistics.
The Cramér-Rao inequality is the primary of the three outcomes of the 1945 paper. When we’re estimating the unknown worth of a parameter, we should pay attention to the estimator’s margin of error. Rao’s work offered a decrease restrict on the variance of an unbiased estimate for a finite pattern. The end result has since change into a cornerstone of mathematical statistics; researchers have prolonged it in many various methods, with functions even in quantum physics, sign processing, spectroscopy, radar techniques, multiple-image radiography, danger evaluation, and chance idea, amongst different fields.
In an article revealed within the journal Statistical Science in 1987, the American statistician Morris H. DeGroot set out an intriguing story (corroborated by Rao’s personal account) of how Rao arrived at the decrease restrict. Prof. Fisher had already established an asymptotic (i.e. when the pattern measurement may be very massive) model of the inequality, and it appears a scholar had requested Rao, “Why don’t you prove it for finite samples?” in 1944. A then-24-year-old Rao did so in below 24 hours!
The second final result of the 1945 paper was the Rao-Blackwell Theorem, which provides a technique to enhance an estimate to an optimum estimate. The Rao-Blackwell theorem and the Cramér-Rao inequality are each associated to the standard of estimators.
A brand new interdisciplinary space referred to as ‘information geometry’ was born as a results of the paper’s third discovering. This subject built-in rules from differential geometry into statistics, together with the ideas of metric, distance, and measure. Erich L. Lehmann, a famend statistician, mentioned in 2008 that “this work [of Rao’s] was before its time and came into its own only in the 1980s”.
So total, Rao’s 1945 paper made an impressive contribution, boosting the event of contemporary statistics and its widespread utility in fashionable analysis. In a 2008 guide, Reminiscences of a Statistician: The Company I Kept, Lehmann additionally mentioned the generative nature of the paper – i.e. the goldmine of insights that it was – and acknowledged that “several of my early papers grew out of Rao’s paper of 1945”.
How did Rao enter the sphere of statistics?
The Australian statistician Terry Speed claimed that the “1940s were ungrudgingly C.R. Rao’s. His 1945 paper … will guarantee that, even had he done nothing else – but there was much else.”
Indeed, one in all Rao’s papers in 1948 supplied a novel generic strategy to testing hypotheses, now extensively referred to as the “Rao score test”. In truth, the three take a look at procedures – the chance ratio take a look at of Jerzy Neyman and E.S. Pearson (1928), the Wald take a look at (1943) of Abraham Wald, and the Rao rating take a look at (1948) – are generally referred to as “the holy trinity” of this department of statistics.
Rao additionally contributed to orthogonal arrays, a idea in combinatorics that’s used to design experiments whose outcomes are qualitatively good, as early as 1949. A 1969 Forbes article described it as “a new mantra” in industrial institutions.
Given the magnitude and relevance of his contributions, it may appear shocking that Rao entered the sphere of statistics by probability.
Despite scoring first in arithmetic at Andhra University, a 19-year-old Rao didn’t safe a scholarship there for administrative causes. He was additionally rejected for a mathematician’s job at a military survey unit as a result of he was judged to be too younger.
When he was staying at a lodge in Calcutta, he met a man who was employed in Bombay and had been despatched to Calcutta to be skilled at the Indian Statistical Institute. He requested Rao to use to the institute as nicely. Rao did so, for a year-long coaching programme in statistics, hoping the extra qualification would assist him land a job.
P.C. Mahalanobis, then director of the institute, replied promptly and Rao was enrolled. That marked the start of a four-decade-long keep at the institute. Rao retired in 1979 and afterwards settled within the U.S.
The first half of the twentieth century was the golden interval of statistical idea typically, and Rao is undoubtedly one of many causes for this being the case, because of his mathematical ingenuity. In the phrases of the late mathematician Samuel Karlin, Rao’s contributions to statistical idea have “earned him a place in the history of statistics”.
Indian statisticians additionally owe Prof. Rao gratitude for his monumental contributions to the expansion of statistics within the nation, notably at the Indian Statistical Institute (the place this creator works). As Lehmann wrote, Rao was “the person who did the most to continue Mahalanobis’s work as a leader of statistics in India.”
Atanu Biswas is professor of statistics, Indian Statistical Institute, Kolkata.
