Studies on statistical sequential estimation problems by the method of sequential analysis

首席调查员和每名调查员都直接或间接地获得了与该项目名称有关的结果。主要研究结果如下：(1)研究了负指数分布未知位置和尺度参数函数的序贯固定宽度区间估计问题。我们提出了一个全序贯过程，并构造了该函数的序贯置信度区间。证明了它的渐近相合性。作为应用，我们考虑了参数比问题，并给出了当可信区间宽度趋于零时上述过程的平均样本量的二阶渐近展开式。给出了一些仿真结果。(2)研究了正态分布均值和标准差未知的线性函数的序列固定宽度区间的收敛速度。我们使用Takada提出的全序贯方法来构造线性函数的序贯可信区间，并研究了当该区间的宽度趋于零时覆盖概率的收敛速度。我们还得到了平均样本量的二阶渐近展开式。

Head investigator and each of investigators obtained the results which are concerned with the title of this project directly or indirectly. The main results given by head investigator are as follows.(1) We consider the sequential fixed-width confidence interval estimation problem for a function of unknown location and scale parameters of a negative exponential distribution. We propose a fully sequential procedure and construct sequential confidence intervals for the function. Its asymptotic consistency is shown. As an application we consider the problem of the ratio of the parameters and give the second-order asymptotic expansion of the average sample size of the above procedure as the width of confidence interval approaches zero. Some simulation results are presented.(2) We consider the convergence rate of sequential fixed-width confidence intervals for a linear function of unknown mean and standard deviation of a normal distribution. We use the fully sequential procedure proposed by Takada to construct sequential confidence intervals for the linear function and investigate the convergence rate of the coverage probability as the width of the confidence interval approaches zero. We also derive a second-order asymptotic expansion of the average sample size.