Sequential determination of estimator as well as sample size
type: Item
instance of: scholarly article
title: Sequential determination of estimator as well as sample size
zbMATH Open document ID: 0544.62075
author: Adam T. Martinsek
published in: The Annals of Statistics
publication date: 1984-01-01T00:00:00Z
review text: Consider the problem of sequential estimation of the location parameter \(\theta\) of a symmetric distribution F with density f. The author obtains an adaptive sequential point estimator as well as a confidence interval for \(\theta\) which are asymptotically efficient with respect to the procedures that use the best trimmed mean as estimator and the best sample size for that trimmed mean. The adaptive estimator as well as the stopping rules are obtained through minimizing the sample variances of \(\alpha\)-trimmed means, \(\alpha \in(0,{1\over2})\). The assumptions imposed on F and f are mild and involve existence of continuous derivatives of \(F^{-1}\) and f. However, the stopping rules proposed may require heavy computation.
Mathematics Subject Classification ID: 62L12
Mathematics Subject Classification ID: 62F25
Mathematics Subject Classification ID: 62F35
zbMATH DE Number: 3866422
zbMATH Keywords: location parameter
zbMATH Keywords: symmetric distribution
zbMATH Keywords: adaptive sequential point estimator
zbMATH Keywords: confidence interval
zbMATH Keywords: best trimmed mean
zbMATH Keywords: best sample size
zbMATH Keywords: stopping rules
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176346504
OpenAlex ID: W2050386346
DOI: 10.1214/AOS/1176346504
description: scientific article; zbMATH DE number 3866422