Vidyadhar Prabakhar Godambe, who died June 9, 2016, is recognized as a pioneer in the foundations of inference in survey sampling.
He is known for formulating and developing a theory of estimating equations. His research contributions, and the fervour with which he pursued the answers to fundamental questions, attracted many other researchers and students to work in the foundations of inference.
Vidyadhar Godambe was born June 1, 1926 in Pune, in the state of Maharashtra in India. He was the second born and the only son in a family of four children. His paternal grandfather was a doctor. He was educated at the Nutan Marathi Vidyalaya, a leading school in Pune, and at Fergusson College for his BSc in mathematics. He was awarded an MSc degree from Bombay University in 1950, and the PhD in 1958 from the University of London. Following a year as Senior Research Fellow at the Indian Statistical Institute in Calcutta, he became Professor and Head of the Statistics Department at Science College in Nagpur, and later held the same post at the Institute of Science, Bombay. In 1964, he left India for North America, his first position being at the Dominion Bureau of Statistics, now Statistics Canada. After visiting appointments at Johns Hopkins University and the University of Michigan, he joined the University of Waterloo in 1967.
While employed as a government statistician before undertaking his PhD, Godambe published the path-breaking paper, “A unified theory of sampling from finite populations”, published in the Journal of the Royal Statistical Society in 1955. This paper provided a theoretical framework for the problem of estimating a survey population total from a probability sample of a subset of the population. This framework led to a result that today we might call “disruptive”, namely that in terms of the optimality criteria in use at the time, there was no best estimator in the class of linear estimators now referred to as the “Godambe class”. Thus the need for new ways of evaluating sampling strategies was established. The framework is still in use; the 1955 paper led to substantial work by Godambe and others on new optimality criteria, and on prescriptions for choosing sampling designs and estimators under various kinds of knowledge of the population.
The late 1950s and early 1960s were a time of re-examination of the foundations of inference in terms of “principles”, by leading statisticians such as G. A. Barnard, A. Birnbaum, D. R. Cox, D. A. S. Fraser and D. A. Sprott. It became clear to Godambe that his formulation of the survey estimation problem brought into sharp relief an apparent contradiction: the likelihood and conditionality principles appeared to be in conflict with “design based estimation”, namely the practice of estimation based on the randomization in the sampling design. Beginning with his 1966 JRSS paper, “A new approach to sampling from finite populations”, he wrote several papers on the riddle of the role of randomized sampling in survey inference, particularly in the presence of a statistical model for the survey responses. His 1982 paper, “Estimation in survey sampling: robustness and optimality”, in the Journal of the American Statistical Association, proposed a resolution of the problem, relating the robustness of design-based inference to the treatment of nuisance parameters in a more traditional statistical model framework. However, in the same year and the same journal, he published the example known as “Godambe’s paradox”. The wide variety of responses to the paradox show that the tension between the principles of inference and the role of randomization persists beyond survey inference, to the very foundations of statistics.
Godambe’s work in the mid-nineteen sixties on the foundations of survey sampling inference attracted attention to the subject, and he provided further impetus by proposing an international conference to bring together survey statisticians and researchers in the foundations of statistics, many of whom would be new to survey sampling. This conference, “New Developments in Survey Sampling”, took place in 1968 at Chapel Hill, North Carolina.
Having arrived at the University of Waterloo, together with David A. Sprott he organized another international symposium on the Foundations of Statistical Inference, which took place in the spring of 1970. He remained in Waterloo thereafter, although he also spent the winter months in India in later years, and kept in touch with colleagues at the University of Pune.
In parallel with his work on survey sampling, he was also making contributions to estimation theory. In 1960 he published the note, “An optimum property of regular maximum likelihood estimation”, in which he defined the notion of an unbiased estimating equation. He introduced an optimality criterion for choosing among estimating functions, and showed that in the one-dimensional parametric case, the maximum likelihood estimating function (and equation) were optimal. There existed already an optimality theory for estimators, based primarily on their properties for very large samples. Godambe’s focus on the estimating function rather than the estimator allowed him from his perspective to formulate and prove optimality results without reference to asymptotics. Subsequent work by Godambe and others developed estimating function methodology into an established framework for estimation.
Godambe’s follow-up work on estimating functions included his 1976 Biometrika paper where what is now known as “Godambe information” was introduced. His application of optimality and information to estimation in stochastic processes had a substantial impact on work in that field.
In his sixth decade of statistical research, Godambe with his collaborators explored the improvement of confidence intervals based on estimating functions, in survey sampling and in time series analysis. Ever drawn to the foundations of inference, he once again took up his long-term interests in causality, and the concept of information in statistics.
Godambe was a Fellow of the Institute of Mathematical Statistics, a Fellow of the American Statistical Association and an Honorary Member of both the Statistical Society of Canada and the International Indian Statistical Association. He was a Platinum Jubilee Lecturer of the 1988 Indian Science Congress, and in 1987 was awarded the Gold Medal of the Statistical Society of Canada. In 2002 he was elected a Fellow of the Royal Society of Canada.
Godambe’s lifelong dedication to research and teaching did not prevent him from being devoted to his
extended family in India and North America, and a good friend to colleagues around the world and members of his community. His enthusiasm for ideas and his infectious laughter will be greatly missed.
Acknowledgements: An article on which this one is based was first requested by the Royal Statistical Society some years ago. Some portions are adapted from an Appendix (by M. Thompson) to the 2006 biography, Philosopher-Statistician: Vidyadhar Godambe, by Chintamani Deshmukh.