Advances in Econometrics and Quantitative Economics.
Essays in Honor of Professor C.R. Rao

Edited by G.S. Maddala, Peter C.B. Phillips, and T.N. Srinivasan
Basil Blackwell Ltd., 1995

Preface

Professor C. R. (Calyampudi Radhakrishna) Rao will be seventy-five on September 10, 1995. This collection of essays celebrates both Professor Rao's many fundamental contributions to statistical foundations of econometrics and his seventy-fifth birthday.

An interesting account of how Professor Rao started to work in statistics can be found in his autobiographical essay (Rao, 1991). He joined the Indian Statistical Institute in 1941, after receiving an MA with a first class and first rank in mathematics from the Andhra University in 1940. He obtained an MA degree in statistics from Calcutta University in 1943 with a first class, first rank and a gold medal. Subsequently he went to Cambridge England to work under R.A. Fisher and was awarded his doctorate in 1948.

A steady stream of original contributions from him began in the early 1940s and continues to flow in good measure to this day. A very early contribution, later to become famous as the Cramér-Rao inequality, was derived by him in 1943 (in a hard night's work in response to the question of a student, V.M. Dandekar, who later became one of India's leading economists). Because of the suspension of the publication of journals in India during the Second World War, this paper (Rao, 1945) was published only in 1945. It contains many other results, including what was later known as the Rao-Blackwell theorem. This paper is also notable for its introduction of differential geometric methods in statistical inference for the first time. It is also perhaps the first attempt to discuss the theme of estimation in small samples in terms of actual variance and methods of obtaining best unbiased estimates.

Econometricians extensively use what they call the LM (Lagrangean Multiplier) test following the terminology introduced by Silvey. In fact, this test is none other than the "score" test introduced in 1947 by Professor Rao ten years before Silvey. Besides the score test, many other tests and techniques in econometrics can be traced to Professor Rao's pioneering work. For example, a very popular test in econometrics that is known as the Hausman test follows from a result (on page 317) of Professor Rao's book Linear Statistical Inference (1973). This book has been translated into six major languages of the world. It is the one most likely to be on the bookshelf of almost every econometrician because it contains an extraordinarily valuable compendium of results in matrix algebra as well as statistical theory. According to the Social Science Citation Index, it is the most cited book in statistics in econometric work.

As Director of the Research and Training School at the Indian Statistical Institute (ISI), Professor C.R. Rao developed a variety of educational programs in the theory and applications of statistics at various levels. Under his leadership, the ISI won international recognition as an outstanding center for theoretical disciplines. His colleagues, students and others who have worked with him at the ISI and elsewhere over the years have experienced his wonderful hospitality and charm and his characteristic modesty. The Times of India (December 31, 1988) chose Professor C.R. Rao to be among the top ten greatest contributors of all time to Indian science.

Professor Rao's many contributions to theoretical statistics in general and multivariate analysis in particular arose from his involvement in the analysis of large data sets at the ISI, such as the Anthropometric Survey in 1941 in the United Provinces of India. He believed with R.A. Fisher that the development of statistical methodology must be firmly rooted in the problems of inference thrown up by actual data. His interest in careful collection and analysis of socioeconomic data led to his founding the Indian Econometric Society to encourage econometric work in India. With his enthusiastic support, the Indian Econometric Society has held seven conferences since 1972 on the database of the Indian economy and has so far published five volumes of conference papers.

We believe that econometricians would find many contributions of Professor Rao useful in their work, and have therefore appended his complete bibliography to this volume. It is hard to do full justice to the many facets of Professor Rao's work in a single volume. The present volume is just a modest contribution by some econometricians in tribute to his work.

References

Rao, C.R. (1945) Information and accuracy attainable in the estimation of statistical parameters. Bulletin of the Calcutta Mathematical Society, 37, 81-91 (also published in Breakthroughs in Statistics, volume 1: Foundations and Basic Theory. New York: Springer-Verlag, pp. 235-48).

Rao, C.R. (1947) Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation. Proceedings of the Cambridge Philosophical Society, 44, 50-7.

Rao, C.R. (1973) Linear Statistical Inference and Its Applications, 2nd edn. New York: Wiley.

Rao, C.R. (1991) Statistics as a Last Resort: an Autobiographical Account of Research Work. Published by T.D. Dwivedi, Concordia University, Montreal.