Greenhouse Joel (ed.) R.R. Bahadur's Lectures on the Theory of Estimation

Institute of Mathematical Statistics, 2002. — 96 p.In the Winter Quarter of the academic year 1984 — 1985, Raj Bahadur gave a series of lectures on estimation theory at the University of Chicago. The role of statistical theory in Chicago's graduate curriculum has always varied according to faculty interests, but the hard and detailed examination of the classical theory of estimation was in those years Raj's province, to be treated in a special topics course when his time and the students' interests so dictated. Winter 1985 was one of those times. In ten weeks, Raj covered what most mathematical statisticians would agree should be standard topics in a course of parametric estimation: Bayes estimates, unbiased estimation, Fisher information, Cramer-Rao bounds, and the theory of maximum likelihood estimation. As a seasoned teacher, Raj knew that mathematical prerequisites could not be taken entirely for granted, that even students who had fulfilled them would benefit from a refresher, and accordingly he began with a review of the geometry of L2 function spaces.In these lectures, Raj Bahadur strived towards, and in most cases succeeded in deriving the most general results using the simplest argument. After stating a result in class, he would usually begin its derivation by saying "it is really simple...", and indeed his argument would often appear to be quite elementary and simple.