The problem of estimating parameters of a Pareto distribution is investigated under a general scale invariant loss function when the scale parameter is restricted to the interval (0, 1]. We consider the estimation of shape parameter when the scale parameter is unknown. Techniques for improving equivariant estimators developed by Stein, Brewster–Zidek and Kubokawa are applied to derive improved estimators. In particular improved classes of estimators are obtained for the entropy loss and a symmetric loss. Risk functions of various estimators are compared numerically using simulations. It is also shown that the technique of Kubokawa produces improved estimators for estimating the scale parameter when the shape parameter is known.

中文翻译：

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帕累托分布参数的改进估计量类别

研究了当尺度参数被限制在（0，1]区间时，在一般尺度不变损失函数下的帕累托分布参数估计问题。考虑尺度参数未知时形状参数的估计。 Stein，Brewster–Zidek和Kubokawa开发的等变估计量被用于推导改进的估计量，特别是获得了熵损失和对称损失的改进估计量，并通过仿真对各种估计量的风险函数进行了数值比较，并显示了久保川的技术产生了改进的估计器，用于在形状参数已知时估计比例参数。