Geodesic
Sequential $d$-guaranteed estimate of the normal mean with bounded relative error
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 161 (2019) no. 1, pp. 145-151

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In this paper, we continue our research on evaluation of the mean value of the normal distribution with prior information that this parameter is positive and very small. These data are obtained by using a prior exponential distribution with a large intensity parameter. The estimation problem with guaranteed relative error is considered. This issue is more important when small fractions are estimated. In addition to restrictions on the relative error, the procedure must have a given level of $d$-risk. We suggest a sequential procedure based on the first achievement by posterior probability of estimate reliability of a given level $1- \beta$. The procedure is adapted to the problem of estimating harmful impurities in food products.
Keywords: first crossing procedure, normal mean estimation, $d$-posterior approach, sequential estimation. 
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     author = {R. F. Salimov and I. N. Volodin and N. F. Nasibullina},
     title = {Sequential $d$-guaranteed estimate of the normal mean with bounded relative error},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
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     publisher = {mathdoc},
     volume = {161},
     number = {1},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2019_161_1_a10/}
}
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R. F. Salimov; I. N. Volodin; N. F. Nasibullina. Sequential $d$-guaranteed estimate of the normal mean with bounded relative error. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 161 (2019) no. 1, pp. 145-151. http://geodesic.mathdoc.fr/item/UZKU_2019_161_1_a10/