Studies on the optimality of methods of statistical sequential decisions

主要研究者和每位研究者直接或间接地获得与本项目标题相关的研究成果。主要研究成果如下：(1)考虑了负指数分布的未知位置和尺度参数线性组合的估计问题。给定一类估计器，我们希望通过使用最小大小的样本来估计线性组合，使得与它们相关的风险不大于预先分配的误差界。我们提出了一个序贯估计量，得到了风险的渐近展开式。(2)考虑k个总体均值线性组合的序贯点估计问题。对于某些类型的分布，与现有的方法相比，我们的方法具有渐近的较小风险。(3)考虑了一个正态分布的未知均值和标准差的线性组合在相对误差平方加上线性代价作为损失函数的情况下的序列点估计问题。我们提出了一类估计量，并得到了相应序列估计量的二阶渐近展开式。

Head investigator and each of the investigators obtained the research results concerning the title of this project directly or indirectly. The main results by head investigator are as follows :(1) We considered the problem of estimating a linear combination of unknown location and scale parameters of a negative exponential distribution. Given a class of estimators, we want to estimate the linear combination by using the sample of the smallest size such that the risk associated with them is not greater than a preassigned error bound. We proposed a sequential estimator and obtained the asymptotic expansion of the risk.(2) We considered the sequential point estimation problem of a linear combination of means of k populations. Our procedure was shown to have asymptotically less risk when compared with the existing procedure for some class of distributions.(3) We considered the sequential point estimation problem of a linear combination of unknown mean and standard deviation of a normal distribution under squared relative error plus linear cost as a loss function. We proposed a class of estimators and obtained second-order asymptotic expansions of the risk associated with the corresponding sequential estimators.