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

首席研究者和每位研究者直接或间接地获得了与本项目标题相关的结果。首席研究员给出的主要结果如下。(1)考虑具有未知位置和尺度参数的负指数分布函数的序贯定宽置信区间估计问题。我们提出了一个完全顺序的过程，并构造了函数的顺序置信区间。证明了其渐近相合性。作为应用，我们考虑了参数的比值问题，并给出了上述过程在置信区间宽度趋近于零时的平均样本量的二阶渐近展开式。给出了一些仿真结果。(2)考虑均值和标准差未知的正态分布线性函数的序贯定宽置信区间的收敛速度。我们使用Takada提出的全序列方法构造线性函数的序列置信区间，并研究了当置信区间宽度趋近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.