On the last time and the number of times an estimator is more than \(\epsilon\) from its target value
Let \(\hat\theta_ n\) be a consistent estimator for a (not necessarily real-valued) parameter \(\theta\). Let \(N_ \varepsilon\) and \(Q_ \varepsilon\) be the last \(n\) and the total number of \(n\) for which \(\hat\theta_ n\) is at least \(\varepsilon\) away from \(\theta\). In this very important and very nice written paper the asymptotic distributions of \(\varepsilon^ 2 N_ \varepsilon\) and \(\varepsilon^ 2 Q_ \varepsilon\) as \(\varepsilon\) goes to zero are obtained. Numerous examples and applications of great importance for statistics are presented.
scientific article; zbMATH DE number 61850