On the last time and the number of times an estimator is more than \(\epsilon\) from its target value
type: Item
instance of: scholarly article
title: On the last time and the number of times an estimator is more than \(\epsilon\) from its target value
zbMATH Open document ID: 0759.62014
author: Nils Lid Hjort
author: Grete Fenstad
published in: The Annals of Statistics
publication date: 1992-09-27T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62L10
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62G20
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 61850
zbMATH Keywords: strongly consistent estimator
zbMATH Keywords: last \(n\)
zbMATH Keywords: limit distributions
zbMATH Keywords: multidimensional parameters
zbMATH Keywords: general distance functions
zbMATH Keywords: maximum likelihood estimator sequence
zbMATH Keywords: sequential tests
zbMATH Keywords: supremum distance
zbMATH Keywords: empirical distribution
zbMATH Keywords: density estimation
zbMATH Keywords: asymptotic optimality
zbMATH Keywords: asymptotic relative efficiency
zbMATH Keywords: Glivenko-Cantelli
zbMATH Keywords: number of epsilon- misses
zbMATH Keywords: sequential confidence regions
zbMATH Keywords: tests with power 1
reviewed by: Ryszard Zieliński
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176348533
OpenAlex ID: W2093001976
DOI: 10.1214/AOS/1176348533
description: scientific article; zbMATH DE number 61850