GENERAL MAXIMUM LIKELIHOOD EMPIRICAL BAYES ESTIMATION OF NORMAL MEANS
GENERAL MAXIMUM LIKELIHOOD EMPIRICAL BAYES ESTIMATION OF NORMAL MEANS
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DOI：
10.1214/08-aos638
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发表时间：
2009-08-01
影响因子：
4.5
通讯作者：
Zhang, Cun-Hui
中科院分区：
文献类型：
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作者：
Jiang, Wenhua;Zhang, Cun-Hui
提出了一种基于I.I.D.观测值估计均值向量的广义极大似然经验贝叶斯方法。正常错误。证明了在未知均值的温和矩条件下，当风险大于(Logn)(5)/n的阶时，当未知均值的长度归一化范数的阶数介于(Logn)(k1/)n(1)/(P Boolean And 2)和n/(Logn)(K2)之间时，广义均值估计的平均均方误差在最小均值的无穷小分数范围内.仿真实验表明，GMLEB在很宽的设置范围内都优于James-Stein和几种最先进的阈值估计器，并且没有太多的负面影响。
We propose a general maximum likelihood empirical Bayes (GMLEB) method for the estimation of a mean vector based on observations with i.i.d. normal errors. We prove that under mild moment conditions on the unknown means, the average mean squared error (MSE) of the GMLEB is within an infinitesimal fraction of the minimum average MSE among all separable estimators which use a single deterministic estimating function on individual observations, provided that the risk is of greater order than (logn)(5)/n. We also prove that the GMLEB is uniformly approximately minimax in regular and weak l(P) balls when the order of the length-normalized norm of the unknown means is between (log n)(k1/)n(1)/((p boolean AND 2)) and n/(logn)(k2). Simulation experiments demonstrate that the GMLEB outperforms the James-Stein and several state-of-the-art threshold estimators in a wide range of settings without much down side.