Improving on the minimum risk equivariant estimator of a location parameter which is constrained to an interval or a half-interval
Improving on the minimum risk equivariant estimator of a location parameter which is constrained to an interval or a half-interval
复制标题
区间或半区间约束的位置参数最小风险等变估计量的改进
DOI：
10.1007/bf02506883
复制
发表时间：
2005
影响因子：
1
通讯作者：
W. Strawderman
中科院分区：
文献类型：
--
作者：
É. Marchand;W. Strawderman
对于密度为f0（x−θ）的位置族，研究了位置不变lossL（θ，d）=ρ（d−θ）的θ估计问题，并在形式θ≥a的下界约束下.我们证明了，对于相当一般的（f0，ρ），关于（a，∞）的一致先验的Bayes估计δ U是一个极小极大估计，它优于基准最小风险同变（MRE）估计.在推广Katz和Farrell的优势估计的基础上，利用Kubokawa的IERD（Integral Expression of Risk Difference）方法，得到了一类包含δ U的优势估计，并用δU刻画了这类估计.最后，研究了上述优势现象，并将其推广到θ∈[a，B]形式的区间约束.
For location families with densitiesf0(x−θ), we study the problem of estimating θ for location invariant lossL(θ,d)=ρ(d−θ), and under a lower-bound constraint of the form θ≥a. We show, that for quite general (f0, ρ), the Bayes estimator δUwith respect to a uniform prior on (a, ∞) is a minimax estimator which dominates the benchmark minimum risk equivariant (MRE) estimator. In extending some previous dominance results due to Katz and Farrell, we make use of Kubokawa'sIERD(Integral Expression of Risk Difference) method, and actually obtain classes of dominating estimators which include, and are characterized in terms of δU. Implications are also given and, finally, the above dominance phenomenon is studied and extended to an interval constraint of the form θ∈[a, b].