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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/135132


    Title: Estimation of mean value of a normal distribution with constraints on the relative error and d-risk
    Authors: 楊素芬
    Yang, Su-Fen
    Salimov, Rustem
    Volodin, Andrei
    Volodin, Igor
    Contributors: 統計系
    Keywords: Parameter estimation;normal mean;d-posterior approach;exponential prior distribution;sequential estimation;estimate with the minimal d-risk;minimal sample size;empirical Bayesian approach
    Date: 2020-02
    Issue Date: 2021-05-25 14:12:21 (UTC+8)
    Abstract: 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.
    Relation: Journal of Statistical Computation and Simulations, Vol.90, No.7, pp.1286-1300
    Data Type: article
    DOI 連結: https://doi.org/10.1080/00949655.2020.1724292
    DOI: 10.1080/00949655.2020.1724292
    Appears in Collections:[國際經營與貿易學系 ] 期刊論文

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