Statistical estimation of non-regular case by Bayesian approach

在一类双边截断分布族的位置参数估计问题中，考虑了每个分布的支撑是一个区间，其密度在区间上为正值，且在端点处为微分系数的情形.然后证明了由极值和一个渐近辅助统计量组成的统计量的二阶渐近信息损失消失。另一方面，从贝叶斯的观点，最佳位置同变估计（皮特曼估计）被视为广义贝叶斯估计，最小化的风险，关于一个不适当的均匀分布和二次损失。在上述估计问题中，我们得到了皮特曼估计的渐近集中概率，并与其它位置同变估计进行了比较。

In the estimation problem on a location parameter for a family of two-sided truncated distributions, we considered the case when each distribution's support is an interval and its density had positive values on the interval and differential coefficients at its endpoints. Then, it was shown that the second order asymptotic loss of information of the statistic consisting of extreme values and an asymptotically ancillary statistic vanished. On the other hand, from the Bayesian viewpoint, the best location equivariant estimator (Pitman estimator) is regarded as the generalized Bayes estimator which minimized the risk with respect to an improper uniform distribution and the quadratic loss. In the above estimation problem, we obtained the asymptotic concentration probability of the Pitman estimator and compared it with other location equivariant estimators.