Statistical estimation of non-regular case by Bayesian approach

在一类双侧截断分布的位置参数估计问题中，我们考虑了当每个分布的支撑点是一个区间，且其密度在区间和端点处的微分系数上均为正值的情况。然后，证明了由极值和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，从贝叶斯的观点出发，将最佳位置等变估计量（Pitman估计量）视为对不均匀分布的风险和二次损失最小化的广义贝叶斯估计量。在上述估计问题中，我们得到了Pitman估计量的渐近集中概率，并将其与其他位置等变估计量进行了比较。

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.