Theoretical Research of Statistical Inference by Multi-Stage Procedures

1.我们证明了构造正态均值的线性函数的固定宽度置信度区间的两阶段过程的渐近二阶有效性。2.我们证明了关于正态平均向量的线性函数的固定区间置信域的两阶段估计的渐近二阶有效性。3.当估计线性损失函数下的正态分布的均值时，我们考虑了多阶段估计过程以达到有界风险。在协方差阵具有一定结构的情况下，给出了多元正态分布均值向量的线性函数的固定区间置信域的两阶段估计。这一过程被证明是渐近二阶有效的。5.我们考虑了一个三阶段过程，该过程被提出来产生具有精确置信度的正态均值的固定宽度的置信度区间。当估计LINEX损失函数下正态均值的线性函数时，我们考虑了一个实现有界风险的序贯点估计过程。为了实现这一目标，引入了一个两阶段估计过程，并检验了它的渐近性质。

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.