A Bayesian Interpretation of Extremum Estimators

Extremum estimation is typically an ad hoc semi-parametric estimation procedure which is only justiied on the basis of the asymptotic properties of the estimators. For a xed nite data set, consider a large number of investigations using diierent extremum estima-tors to estimate the same parameter vector. The resulting empirical distribution of point estimates can be shown to coincide with a Bayesian posterior measure on the parameter space induced by a minimum information procedure. The Bayesian interpretation serves a number of purposes ranging from lending legitimacy to the use of those procedures in small sample problems, to helping prove asymptotic properties by reference to Bayes central limit theorems, to laying a foundation for combining point estimates from various extremum estimation experiments for statistical decision processes. for their many useful comments. I am also grateful to an anonymous referee for a number of useful suggestions. Any remaining errors are, of course, my own.