SHRINKAGE EFFICIENCY BOUNDS
SHRINKAGE EFFICIENCY BOUNDS
复制标题
收缩效率界限
作者：
B. Hansen
本文是Magnus（2002，Econometrics Journal 5，225-236）的多维扩展。本文考虑了在平方误差损失下多元正态均值的估计.在满足Efron和Morris（1976，Annals of Statistics 4，11-21）充分条件的极小极大正交不变估计类中，我们构造了极小极大收缩估计的效率界（最低可实现风险）.这使我们能够比较现有的正交不变收缩估计的遗憾。我们还构造了一个新的收缩估计，实现了大大低于现有的估计最大遗憾。
This paper is an extension of Magnus (2002, Econometrics Journal 5, 225–236) to multiple dimensions. We consider estimation of a multivariate normal mean under sum of squared error loss. We construct the efficiency bound (the lowest achievable risk) for minimax shrinkage estimation in the class of minimax orthogonally invariate estimators satisfying the sufficient conditions of Efron and Morris (1976, Annals of Statistics 4, 11–21). This allows us to compare the regret of existing orthogonally invariate shrinkage estimators. We also construct a new shrinkage estimator which achieves substantially lower maximum regret than existing estimators.