Geodesic
On the location parameter confidence intervals based on a~random size sample from a~partially known population
Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part 10, Tome 207 (1993), pp. 98-100

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The problem of constructing confidence intervals of a fixed length for the location parameter based on a random size sample is considered. It is proposed to use the confidence interval $$ \theta^*-u\sqrt p/\sigma\theta\theta^*+u\sqrt p/\sigma, $$ where $\theta^*$ is an adaptive estimator, $\sigma^2$ is the Fisher information, and $p^{-1}$ is the mean of the sample size. Nonparametric bounds are given for the limit as $p\to0$ confidence probability. Bibliography: 5 titles. 
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     author = {L. B. Klebanov and J. A. Melamed},
     title = {On the location parameter confidence intervals based on a~random size sample from a~partially known population},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {98--100},
     publisher = {mathdoc},
     volume = {207},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1993_207_a6/}
}
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L. B. Klebanov; J. A. Melamed. On the location parameter confidence intervals based on a~random size sample from a~partially known population. Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part 10, Tome 207 (1993), pp. 98-100. http://geodesic.mathdoc.fr/item/ZNSL_1993_207_a6/