A sequential analytic approach to the methods of optiaml statistical decisions

首席调查员和每位调查员直接或间接获得了关于该项目名称的研究结果。主要研究结果如下：(1)对于均值积分平方误差为预定界的非参数概率密度函数的估计问题，我们提出了序贯密度估计量，并证明了其渐近有效性。(2)对于均值和方差均未知的正态分布的均值和标准差的线性组合，我们考虑了序贯固定宽度的区间估计。构造了给定固定宽度和覆盖概率的序贯置信度区间及其渐近相合性。(3)考虑了相对误差平方和线性代价下非零均值的序贯点估计为损失函数。我们提出了一个序贯过程，并证明了对于某一类分布，该过程比已有过程具有更小的风险。(4)在一定的损失函数下，我们考虑了负指数分布尺度参数的有界风险点估计问题。我们提出了两个序贯估计，并给出了与之相关的风险的渐近展开式。

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) For the problem of estimating nonparametric probability density function with preassigned bound of mean integrated squared error we proposed sequential density estimators, and showed their asymptotic efficiency.(2) We considered sequential fixed-width confidence interval estimation for a linear combination of mean and standard deviation of a normal distribution with mean and variance both unknown. We constructed sequential confidence intervals with preassigned fixed-width and coverage probability, and their asymptotic consistency.(3) We considered the sequential point estimation of the nonzero mean under squared relative error plus linear cost as a loss function. We proposed a sequential procedure and showed this procedure has a risk less than that of the existing procedure for a certain clas of distributions.(4) We considered the problem of bounded risk point estimation for the scale parameter of a nagative exponential distribution under a certain loss function. We proposed two sequential estimators, and gave the asymptotic expansions of the risk associated with them.