On a Conjecture of Krishnamoorthy and Gupta
On a Conjecture of Krishnamoorthy and Gupta
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论克里希纳莫西和古普塔的猜想
DOI：
10.1006/jmva.1997.1683
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发表时间：
1997
影响因子：
1.6
通讯作者：
François Perron
中科院分区：
文献类型：
--
作者：
François Perron
我们考虑估计精度矩阵（？？1)在完全不变的凸损失下。假设存在极小极大常数风险估计量？(say)解决这个问题。K. Krishnamoorthy和A. K.古普塔提出了一个操作，将这个估计到一个正交不变的估计？* (say)他们有这样的推测吗 *也是极大极小。本文共分两部分。在第一部分中，我们提出了反例。在第二部分中，我们阐述了一种技术，可以用来证明某些估计是极小极大。这种技术，然后成功地应用到一些估计提出的Krishnamoorthy和古普塔文件。
We consider the problem of estimating the precision matrix (??1) under a fully invariant convex loss. Suppose that there exists a minimax constant risk estimator?(say) for this problem. K. Krishnamoorthy and A. K. Gupta have proposed an operation which transforms this estimator into an orthogonally invariant estimator?* (say) and they have a conjecture saying that?* is minimax as well. This paper contains two parts. In the first part, we present counterexamples. In the second part, we elaborate a technique which can be used to prove that certain estimators are minimax. This technique is then applied successfully to some of the estimators proposed in the Krishnamoorthy and Gupta paper.