@article{oai:tsukuba.repo.nii.ac.jp:00025207,
 author = {青嶋, 誠 and 矢田, 和善 and Aoshima, Makoto and Yata, Kazuyoshi},
 issue = {3},
 journal = {Annals of the Institute of Statistical Mathematics},
 month = {Jun},
 note = {We consider fixed-size estimation for a linear function of means from
independent and normally distributed populations having unknown and respective
variances.We construct a fixed-width confidence interval with required accuracy about
the magnitude of the length and the confidence coefficient. We propose a two-stage
estimation methodology having the asymptotic second-order consistency with the
required accuracy. The key is the asymptotic second-order analysis about the risk
function.We give a variety of asymptotic characteristics about the estimation methodology,
such as asymptotic sample size and asymptotic Fisher-information. With the
help of the asymptotic second-order analysis, we also explore a number of generalizations
and extensions of the two-stage methodology to such as bounded risk point
estimation, multiple comparisons among components between the populations, and
power analysis in equivalence tests to plan the appropriate sample size for a study.},
 pages = {571--600},
 title = {Asymptotic second-order consistency for two-stage estimation methodologies and its applications},
 volume = {62},
 year = {2010}
}