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Estimation of the Mean Value for the Normal Distribution with Constraints on d-Risk

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dc.date.accessioned 2019-01-22T20:51:33Z
dc.date.available 2019-01-22T20:51:33Z
dc.date.issued 2018
dc.identifier.issn 1995-0802
dc.identifier.uri https://dspace.kpfu.ru/xmlui/handle/net/149128
dc.description.abstract © 2018, Pleiades Publishing, Ltd. We consider the problem of an estimation of the mean value of the normal distribution with a prior information that this parameter is positive and very small. The prior information is implemented in terms of the exponential prior distribution. The estimation procedures are constructed for two cases: fixed sample size and sequential estimation that guarantee the given constraints on the precision and the d-risk of the estimator. An analytical review of the comprehensive literature for the problems of guaranteed statistical inference (d-risk and pFDR) is provided. For the practical applications of the proposed estimators with the unknown value of the prior distribution parameter, we solve the problem of choosing this parameter in the framework of empirical (parametric) Bayesian approach or in the framework of existing State Standards on the precision and output quality of the estimated parameter. As an implementation of the proposed statistical procedures, the problem of estimation of the chemical element of arsenic (As) in a food product is considered. The model parameters are chosen according to the State Standards for carrying out a laboratory tests for As detection. For the chosen values of the parameters, the probability of stopping for the experiment is estimated for each step by the method of statistical simulations. The histogram of the Bayesian estimate for the As content is presented.
dc.relation.ispartofseries Lobachevskii Journal of Mathematics
dc.subject d-posterior approach
dc.subject empirical Bayesian approach
dc.subject exponential prior distribution
dc.subject normal mean
dc.subject Parameter estimation
dc.subject sequential estimation
dc.title Estimation of the Mean Value for the Normal Distribution with Constraints on d-Risk
dc.type Article
dc.relation.ispartofseries-issue 3
dc.relation.ispartofseries-volume 39
dc.collection Публикации сотрудников КФУ
dc.relation.startpage 377
dc.source.id SCOPUS19950802-2018-39-3-SID85045657879


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  • Публикации сотрудников КФУ Scopus [24551]
    Коллекция содержит публикации сотрудников Казанского федерального (до 2010 года Казанского государственного) университета, проиндексированные в БД Scopus, начиная с 1970г.

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