Asymptotic results in robust quasi-Bayesian estimation (Q1109450)

Let \(\theta\) be a real random variable with a known (a priori) distribution. The problem is to estimate \(\theta\) after observing \(X_ 1,...,X_ n\), when \(X_ 1-\theta\), \(X_ 2-\theta,...\), given \(\theta\), are independent, identically distributed random variables with a common distribution function F. It is known that F belongs to some family \({\mathcal F}\) of distributions on the real line. The author imposes a set of conditions on \({\mathcal F}\), including the existence of an asymptotically minimax sequence of estimators in the frequentist sense, and uses these estimators to construct asymptotically minimax Bayes estimators of \(\theta\) for bounded and unbounded loss functions.