Sequential simultaneous estimation of the mean and variance: The rate of convergence
type: Item
instance of: scholarly article
title: Sequential simultaneous estimation of the mean and variance: The rate of convergence
zbMATH Open document ID: 0606.62089
DOI: 10.1007/BF01894759
author: G. Vik
author: Nitis Mukhopadhyay
published in: Metrika
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/176066
review text: Suppose \(X_ 1,X_ 2,...\), is a sequence of i.i.d. random variables each distributed \(N(\mu,\sigma^ 2)\) where both parameters \(\mu\) and \(\sigma^ 2\) are unknown. The authors consider the problem of simultaneous estimation of \(\mu\) and \(\sigma^ 2\). They define stopping rules in this estimation problem and derive the rate of convergence of the corresponding normalized quantities to normality. Other interesting topics are discussed too.
Mathematics Subject Classification ID: 62L12
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 3980292
zbMATH Keywords: mean
zbMATH Keywords: variance
zbMATH Keywords: Berry-Esseen type results for randomly stopped U- statistics
zbMATH Keywords: normal distribution
zbMATH Keywords: simultaneous estimation
zbMATH Keywords: stopping rules
zbMATH Keywords: rate of convergence
reviewed by: Jordan Stoyanov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3980292