Theoretical Research of Statistical Inference by Multi-Stage Procedures

1.我们展示了一个两阶段过程的渐近二阶效率，该过程被提出用于构造一个固定宽度的正态均值线性函数的置信区间。我们证明了关于正态均值向量的线性函数的定跨度置信区域的两阶段估计的渐近二阶效率。在估计LINEX损失函数下正态分布的均值时，我们考虑了多阶段估计程序来实现有界风险。介绍了两阶段估计和三阶段估计，并对它们的二阶渐近性进行了检验。当协方差矩阵具有一定结构时，给出了多元正态分布均值向量线性函数的定跨度置信域的两阶段估计。证明了该方法是渐近二阶有效的。我们考虑了一个三阶段的程序，该程序被提议产生具有精确置信水平的正态均值的固定宽度置信区间。证明了该过程是渐近二阶有效的。我们考虑了一个序贯的点估计过程，以达到在线性损失函数下估计正态均值的线性函数时的有界风险。为了实现这一目标，引入了一种两阶段估计方法，并检验了其渐近性。

1.We showed an asymptotic second-order efficiency of a two-stage procedure which was proposed to construct a fixed-width confidence interval for a linear function of normal means.2.We showed an asymptotic second-order efficiency of a two-stage estimation for a fixed-span confidence region about a linear function of normal mean vectors.3.We considered multistage estimation procedures to achieve a bounded risk when estimating the mean of a normal distribution under a LINEX loss function. Two-stage and three-stage estimation procedures are introduced and their second-order asymptotic was examined.4.We proposed a two-stage estimation for a fixed-span confidence region about a linear function of mean vectors of multivariate normal distributions when the covariance matrices have some structures. The procedure was shown to be asymptotically second-order efficient.5.We considered a three-stage procedure which was proposed to yield a fixed-width confidence interval of the normal mean with a precise confidence level. The procedure was shown to be asymptotically second-order efficient.6.We considered a sequential point estimation procedure to achieve a bounded risk when estimating a linear function of normal means under a LINEX loss function. A two-stage estimation procedure was introduced to achieve the goal and its asymptotic property was examined.