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Estimation of mean value of a normal distribution with constraints on the relative error and d-risk

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dc.contributor.author Salimov R.
dc.contributor.author Yang S.F.
dc.contributor.author Volodin A.
dc.contributor.author Volodin I.
dc.date.accessioned 2021-02-25T20:33:35Z
dc.date.available 2021-02-25T20:33:35Z
dc.date.issued 2020
dc.identifier.issn 0094-9655
dc.identifier.uri https://dspace.kpfu.ru/xmlui/handle/net/161732
dc.description.abstract © 2020, © 2020 Informa UK Limited, trading as Taylor & Francis Group. We consider a problem of mean value estimation for a normal distribution with prior knowledge of its randomness and extreme smallness. We continue our investigation presented in article [Volodin et al. Estimation of the mean value for the normal distribution with constrains on d-risk. Lobachevskii J Math. 2018;39:377–387], where the constraints have been made on the absolute estimation error. It is more appropriate to control its relative estimation error, not the absolute. In this article, we consider not only estimates based on a fixed number of observations, but also the sequential procedure of estimation. Both estimators guarantee the given constraints on their d-risks (the so-called d-guarantee procedure). We present a simple method for calculating the minimal sample size that guarantees the given constraints on the d-risk of the relative error when the estimators with uniformly minimal d-risk and Bayesian are applied. A sequential guarantee estimation procedure is also proposed, and the distribution of the corresponding stopping time is illustrated by the results of statistical simulations. As a practical application of the proposed statistical procedures, the problem of estimating the concentration of arsenic in drinking water is considered.
dc.relation.ispartofseries Journal of Statistical Computation and Simulation
dc.subject d-posterior approach
dc.subject empirical Bayesian approach
dc.subject estimate with the minimal d-risk
dc.subject exponential prior distribution
dc.subject minimal sample size
dc.subject normal mean
dc.subject Parameter estimation
dc.subject sequential estimation
dc.title Estimation of mean value of a normal distribution with constraints on the relative error and d-risk
dc.type Article
dc.relation.ispartofseries-issue 7
dc.relation.ispartofseries-volume 90
dc.collection Публикации сотрудников КФУ
dc.relation.startpage 1286
dc.source.id SCOPUS00949655-2020-90-7-SID85079236948

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  • Публикации сотрудников КФУ Scopus [22633]
    Коллекция содержит публикации сотрудников Казанского федерального (до 2010 года Казанского государственного) университета, проиндексированные в БД Scopus, начиная с 1970г.

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