RESEARCH OF STATISTICAL INFERENCE PLANS ON THE BASIS OF SOME PRIOR

这项研究涉及估计参数的情况，其中一个人有关于参数的先验信息的形式的初步猜想区间。它基于最小判别信息(MDI)方法，旨在提出和开发一种比通常的估计器(M.L.E.)具有更低风险的估计器。在或超出猜想的区间内。对于1997年的二项分布参数和1998年的二元正态均值向量的参数估计，得到了MDI估计量及其变种。这些都产生了一类收缩类型估计，它向初步猜测的区间收缩。在二次损失函数下对它们的风险进行了评估，并与通常的估计值进行了比较。给出了所提出的估计量的有利性质，并对它们的使用提出了建议。

This research is concerned with estimating a parameter for the case where one has a prior information about the parameter in the form of preliminary conjectured intervals. It is based on the minimum discrimination information(MDI) approach, intended to propose and develop an estimator that has lower risk than the usual estimator (m.l.e.) in or beyond the conjectured intervals. A MDI estimator and its variants were obtained for the estimation of the parameter about the binomial distribution in 1997 and that of the bivariate normal mean vector in 1998. These yield a class of shrinkage type estimator that shrinks towards the preliminary conjectured interval. Their risks were evaluated and compared with the usual estimator under a quadratic loss function. Favorable properties of the proposed estimators were given and recommendations for their use were also made.