 Modifying Estimators of Ordered Positive Parameters under the Stein LossHisayuki Tsukuma and
Tatsuya Kubokawa
No CIRJE-F-510, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo Abstract: This paper treats the problem of estimating positive parameters restricted to a polyhedral convex cone which includes typical order restrictions such as simple order, tree order and umbrella order restrictions. In this paper, two methods are used to show the improvement of order-preserving estimators over crude non-order-preserving estimators without any assumption on underlying distributions. One is to use Fenchel's duality theorem, and then the superiority of the isotonic regression estimator is established under the general restriction to polyhedral convex cones. The use of the Abel identity is the other method, and we can derive a class of improved estimators which includes order-statistics-based estimators in the typical order restrictions. When the underlying distributions are scale families, the unbiased estimators and their order-restricted estimators are shown to be minimax. The minimaxity of the generalized Bayes estimator against the prior over the restricted space is also demonstrated in the two dimensional case. Finally, some examples and multivariate extensions are given. Pages: 28 pages There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2007cf510 Access Statistics for this paper More papers in CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo Contact information at EDIRC. |
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