著者

Aoshima Makoto Yata Kazuyoshi

出版者

Springer

雑誌

Annals of the Institute of Statistical Mathematics (ISSN:00203157)

巻号頁・発行日

vol.62, no.3, pp.571-600, 2010-06

被引用文献数

11

---

We consider fixed-size estimation for a linear function of means fromindependent and normally distributed populations having unknown and respectivevariances.We construct a fixed-width confidence interval with required accuracy aboutthe magnitude of the length and the confidence coefficient. We propose a two-stageestimation methodology having the asymptotic second-order consistency with therequired accuracy. The key is the asymptotic second-order analysis about the riskfunction.We give a variety of asymptotic characteristics about the estimation methodology,such as asymptotic sample size and asymptotic Fisher-information. With thehelp of the asymptotic second-order analysis, we also explore a number of generalizationsand extensions of the two-stage methodology to such as bounded risk pointestimation, multiple comparisons among components between the populations, andpower analysis in equivalence tests to plan the appropriate sample size for a study.