Methodology of sequential procedures and its applications

主要研究结果如下：(1)在尺度参数的正下界已知的假设下，我们考虑了负指数分布位置参数的固定宽度可信区间估计问题。利用MukHopadhyay和Duggan(1999)提出的两阶段法，我们给出了平均样本数和覆盖概率的高阶渐近展开式。(2011)(2)在未知方差的正下界已知的假设下，我们考虑了正态总体均值和方差的最小风险点估计问题。利用两阶段法，我们给出了高于二阶近似的平均样本数和后悔程度。

The main results which head investigator obtained are as follows.(1) We consider the problem of fixed-width confidence interval estimation of a location parameter of a negative exponential distribution under the assumption that a positive lower bound of a scale parameter is known. Using the two-stage procedure proposed by Mukhopadhyay and Duggan (1999) we provided higher order asymptotic expansions of the average sample number and coverage probability. (2011) (2) We considered the minimum risk point estimation problem for the mean and variance of a normal population under the assumption that a positive lower bound of an unknown variance is known. By using two-stage procedure we gave higher than second-order approximations of the average sample number and regret.(2013)