Studies on efficiency of statistical methods of sequential estimation

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)考虑指数分布尺度参数函数的最小风险序贯点估计问题，其损失函数为误差平方和和线性代价。我们希望通过使用使损失预期风险最小化的样本量来估计函数。最小的样本量包含未知参数。因此，我们提出了一个完全顺序过程，并给出了单位观测成本趋于零时期望样本量和风险的二阶展开式。(2)考虑了从两个指数总体估计两个尺度参数函数的问题。我们想构造一个具有给定长度和置信系数的函数的置信区间。由于最优最小样本量中包含未知参数，因此我们提出了全序贯抽样方法和序贯置信区间。我们证明了这些序列置信区间具有渐近一致性，并给出了期望样本量的二阶渐近展开式。(3)考虑两个指数分布尺度参数之比的序贯有界风险点估计，其受给定损失函数的影响为平方误差。我们希望在预期损失的风险由一个预先指定的正常数限定的条件下估计比率。满足条件的最小样本量包含未知参数。因此，我们提出了一个全序贯抽样方案，并提供了期望样本量和序贯过程风险的二阶近似。我们还提出了一种偏差校正顺序程序来降低风险，并获得了其风险的二阶近似。少

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 considered the minimum risk sequential point estimation problem for a function of the scale parameter of an exponential distribution subject to the loss function given as a sum of the squared error and a linear cost. We want to estimate the function by using the sample size which minimizes the risk of the expectation of the loss. Then the smallest sample size contains the unknown parameter. Therefore, we proposed a fully sequential procedure and gave the second-order expansion of the expected sample size and risk when the cost per unit observation tended to zero.(2) We considered the problem of estimating a function of two scale parameters from two exponential populations. We want to construct a confidence interval of the function with given length and confidence coefficient. The asy … More mptotic smallest sample size contains the unknown parameters, so we proposed a fully sequential sampling procedure and sequential confidence intervals. We showed that these sequential confidence intervals have asymptotic consistency and gave the second-order asymptotic expansion of the expected sample size.(3) We considered sequential bounded risk point estimation of the ratio of scale parameters of two exponential distributions subject to the loss function given as the squared error. We wish to estimate the ratio under the condition that the risk of the expected loss is bounded by a preassigned positive constant. The smallest sample size which satisfies the condition includes the unknown parameters. Therefore, we proposed a fully sequential sampling scheme and provided second order approximation of the expected sample size and the risk of the sequential procedure. We also proposed a bias corrected sequential procedure to reduce the risk and obtained a second order approximation of its risk. Less