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Asymptotic second-order consistency for two-stage estimation methodologies and its applications
en
Aoshima Makoto
Yata Kazuyoshi
青嶋 誠
矢田 和善
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.
Annals of the Institute of Statistical Mathematics
62
3
571-600
2010-06
0020-3157
AA00026236
10.1007/s10463-008-0188-y
© The Institute of Statistical Mathematics, Tokyo 2008. The original publication is available at www.springerlink.com
数学
Springer
http://hdl.handle.net/2241/114080