On stochastic estimation
The author considers a sequence (\({\mathcal X}_ n,{\mathcal B}_ n,(P_{n,\theta})\), \(\theta \in \Theta \subset {\mathbb{R}}^ k)\) of experiments; \({\mathcal X}_ n\) is a metric space, \(\Theta\) an open subset of \({\mathbb{R}}^ k\), and \(T_ n:{\mathcal X}_ n\times \Theta \to {\mathbb{R}}^ m\) a statistic. He is interested in estimators \(\{\) \({\hat \theta}{}_ n\}\) which have the following property: \[ (*)\quad T_ n(\cdot,{\hat \theta}(\cdot))\to 0\quad in\quad P_{n,\theta}\quad probability. \] By a local random search procedure his aim is to improve a sequence \(\{\) \({\bar \theta}{}_ n\}\) of estimators which is \(\sqrt{n}\)-consistent, in such a way that the improved version has property (*) and is asymptotically equivalent to \({\hat \theta}{}_ n\) up to order 1/\(\sqrt{n}\).
scientific article; zbMATH DE number 4124841