Purely sequential bounded-risk point estimation of the negative binomial mean under various loss functions: one-sample problem
type: Item
instance of: scholarly article
title: Purely sequential bounded-risk point estimation of the negative binomial mean under various loss functions: one-sample problem
zbMATH Open document ID: 1406.62089
author: Nitis Mukhopadhyay
author: Sudeep R. Bapat
published in: Annals of the Institute of Statistical Mathematics
publication date: 2018-09-25T00:00:00Z
review text: The paper provides a purely sequential, bounded-risk methodology [\textit{L. J. Willson} and \textit{J. L. Folks}, Commun. Stat., Sequential Anal. 2, 55--70 (1983; Zbl 0594.62095); \textit{S. Zacks}, Stage-wise adaptive designs. Hoboken, NJ: John Wiley \& Sons (2009; Zbl 1171.62065)] to estimate an unknown mean \(\mu\) of the negative binomial distribution under different forms of loss functions. The list of the considered loss functions includes Linex loss (customary and modified) and the squared error loss. The cases of an unknown and known thatch parameter \(\tau\) is handled. It is shown that the proposed approach satisfies the first order asymptotic efficiency and the first-order asymptotic risk efficiency. The proposed methodologies have been checked based on small and moderate sample sizes sets of simulations. The real data from statistical ecology are also treated by these estimation strategies.
reviewed by: Krzysztof J. Szajowski
Mathematics Subject Classification ID: 62L12
Mathematics Subject Classification ID: 62L10
Mathematics Subject Classification ID: 62P12
zbMATH DE Number: 6943458
zbMATH Keywords: Linex loss
zbMATH Keywords: CV approach
zbMATH Keywords: first-order asymptotic efficiency
zbMATH Keywords: first-order asymptotic risk efficiency
zbMATH Keywords: migrating woodlarks data
zbMATH Keywords: over-dispersed count data
zbMATH Keywords: squared error loss
zbMATH Keywords: statistical ecology
zbMATH Keywords: weed count data
zbMATH Keywords: bird sanctuary data
describes a project that uses: R
MaRDI profile type: Publication
full work available at URL: s10463-017-0620-2
OpenAlex ID: W2764332264
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DOI: 10.1007/S10463-017-0620-2
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description: scientific article; zbMATH DE number 6943458