On stochastic estimation
type: Item
instance of: scholarly article
title: On stochastic estimation
zbMATH Open document ID: 0686.62065
DOI: 10.1007/BF00053062
author: Jens-Peter Kreiß
published in: Annals of the Institute of Statistical Mathematics
publication date: 1988-01-01T00:00:00Z
review text: 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/\(\sqrt{n}\).
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 65C05
zbMATH DE Number: 4124841
zbMATH Keywords: first order autoregressive processes
zbMATH Keywords: simulation results
zbMATH Keywords: local asymptotic normality
zbMATH Keywords: local random search procedure
MaRDI profile type: Publication
cites work: Stochastic estimation and testing
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full work available at URL: https://doi.org/10.1007/bf00053062
OpenAlex ID: W2093549897
description: scientific article; zbMATH DE number 4124841