Theoretical Research of Statistical Inference by Multi-Stage Procedures

1.证明了正态均值线性函数的固定宽度置信区间的两阶段估计的渐近二阶有效性. 2.证明了正态均值线性函数的固定宽度置信区间的两阶段估计的渐近二阶有效性. 3.在估计正态均值向量的线性函数时，我们考虑了多阶段估计过程，以实现有界风险。LINEX损失函数下的正态分布。给出了两阶段和三阶段估计方法，并研究了它们的二阶渐近性质。4.当协方差矩阵具有某种结构时，给出了多元正态分布均值向量线性函数的固定跨度置信域的两阶段估计。该方法是渐近二阶有效的。5.我们考虑了一个三阶段的方法，提出了一个固定宽度的置信区间的正态均值与精确的置信水平。6.在LINEX损失函数下，我们考虑了一个序贯点估计方法来估计正态均值的线性函数，以达到有界风险。一个两阶段的估计过程被引入到实现的目标和它的渐近性质进行了检查。

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.