Professor Basu, in his long illustrious career, has made many fundamental contributions to the foundations of statistical inference. Among others, I point out his work on ancillarity, likelihood principle, partial and marginal sufficiency, randomization and foundations of survey sampling.
In spite of all the above contributions, Basu is possibly the most well-known to a vast majority of statisticians for a theorem which bears his name. Basu’s Theorem, published in
, 1955, has served several generations of statisticians as a fundamental tool for proving independence of statistics. The theorem itself is beautiful because of its elegance and simplicity, and yet one must acknowledge its underlying depth, as it is built on several fundamental concepts of statistics, such as sufficiency, completeness and ancillarity.