C.R.Rao: Statistical genius, teacher, institution-builder

India’s tragedy is that teachers of statistics only produce other teachers of statistics these days, a former head of the National Statistical Commission (NSC) said to me recently, pointing to the rupture between the worlds of official and academic statistics. In contrast, in the early years of the republic, leading statisticians of the day helped build India’s official statistical system. Statistical research in academia in turn was driven by real-life problems encountered in policy-making and industrial operations.

There is no better example of an Indian statistician who contributed equally to statistical theory and practice than Calyampudi Radhakrishna Rao. A living legend who made fundamental contributions to mathematical statistics and econometrics, Rao helped in the design of the National Sample Survey (NSS) and took charge of training the early generations of official statisticians from India and other parts of the world at the Indian Statistical Institute (ISI).

P.C. Mahalanobis, ISI’s founder and the lead architect of India’s statistical system, asked Rao to lead ISI’s research and training wing, making him a professor at a young age of 29. Rao set up the International Statistical Education Centre at ISI, where statisticians from other parts of the world arrived to learn from the Indian pioneers of ‘statistical engineering’. The UN Statistical Institute for Asia and the Pacific at Tokyo was also established on Rao’s recommendation.

Rao made sure that statistical practitioners received training through practical examples rather than through derivation of statistical theorems. He played as important a role in realizing Mahalanobis’ mission as Swami Vivekananda played in fulfilling Ramkrishna Paramahamsa’s, another statistician would comment years later.

Apart from training official statisticians, Rao also helped train the first generation of quality control experts in the country. Government officials did not fully understand the significance of operations research and quality control. But factory managers understood its potential. Rao’s own theoretical work on orthogonal arrays played a key role in the development of the theory of industrial quality control. The ‘Taguchi method’ of quality control, which came to be used by several multinational firms globally, was built on the foundations laid by Rao.

Rao is perhaps the most-widely cited Indian scholar in statistics and econometrics textbooks globally, with many key theorems and concepts bearing his name, the Cramer-Rao lower bound and Rao-Blackwell theorem being the most famous. Of the so-called ‘holy trinity’ of tests used to gauge the strength of regression models, the score-test (known to most econometricians as the ‘Lagrange multiplier’ test) was first devised by Rao. His early work helped develop the field of information geometry, which is now finding application in machine learning tools.

Rao played as big a role in catalysing new thinking on practical data problems as he did in pushing the frontiers of theoretical statistics. He set up The Indian Econometric Society (TIES) in 1970 and organized a series of workshops under its aegis in the early 1970s to assess the state of India’s official statistical system. This was perhaps the last such effort by an independent statistician. Debates on official statistics since then have largely been among economists. Barring those performing official duties in the statistical system, statisticians have been missing from such debates.

Rao was born in 1920 to a policeman’s family in Madras province, and faced the taste of caste discrimination as a young non-Brahmin student early in life. At ISI, Bengali co-workers were not always very kind. In a 2003 interview to Anil Bera published in the journal Econometric Theory, Rao recalled how Mahalanobis consoled him using Tagore’s words when he faced such discrimination. Those words were from Tagore’s poem Bangamata, which ends with a lament that ‘Mother Bengal’ had raised her 70 million children as Bengalis, not as human beings.

Rao too was an accidental statistician like Mahalanobis and P.V. Sukhatme. He had come to Calcutta in 1940 to apply for an army mathematician’s job but was turned down. A chance encounter led him to ISI, where Mahalanobis accepted him as a student. Rao later studied under R.A. Fisher in Cambridge, extending Mahalonobis’ work on multivariate analysis.

Mahalanobis’ support kept Rao at ISI till his retirement. Rao’s relationship with ISI’s new management deteriorated after Mahalanobis’ death, and led him to move to the US, where he received a warm welcome. His ‘post-retirement’ academic career has been even more prolific, with Rao becoming an early proponent of a ‘data science’ approach to statistical problems. Many of Rao’s students have gone on to make important contributions to the discipline.

Rao has always been an excellent communicator and his 1997 book Statistics and Truth: Putting Chance to Work remains one of the most accessible introductions to the subject. In an information age, statistical reasoning is important for an average citizen to guard against the politician’s propaganda and the businessman’s advertisements, Rao wrote. He also stressed the need for a new kind of statistical journalism in his book.

Rao, who turns 102 next month, is perhaps the country’s last surviving link with its rich statistical heritage.

This is the concluding part of a five-part series on the founders of India’s once-renowned statistical system.

Pramit Bhattacharya is a Chennai-based journalist. His Twitter handle is pramit_b