On the location parameter confidence intervals based on a random size sample from a partially known population

L. B. Klebanov   ; J. A. Melamed

Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part 10, Tome 207 (1993), pp. 98-100

Résumé

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.