Estimation of the entropy of a multivariate normal distribution
Estimation of the entropy of a multivariate normal distribution
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DOI：
10.1016/j.jmva.2003.10.003
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发表时间：
2005-02-01
影响因子：
1.6
通讯作者：
Demchuk, E
中科院分区：
文献类型：
--
作者：
Misra, N;Singh, H;Demchuk, E
在分子生物科学中，分子系统的熵的评估是很重要的，了解其热力学性质的问题的启发，我们认为有效的估计熵的多元正态分布具有未知的平均向量和协方差矩阵。基于随机样本，讨论了二次损失函数下的熵估计问题。最好的仿射同变估计，有趣的是，它也原来是一个无偏估计和广义贝叶斯估计。证明了最佳仿射同变估计在仅依赖于样本协方差矩阵行列式的估计类中是可容许的。最好的仿射同变估计的最大似然估计（分子科学中常用的估计）的风险改善得到数值，并被发现是大量的更高的维度，这是通常的情况下，在大分子，如蛋白质的原子坐标。进一步证明了即使是最好的仿射同变估计也是不可容许的，并得到了Stein型和Brewster-Zidek型估计，证明了Brewster-Zidek型估计是广义Bayes估计. (C)2003年爱思唯尔公司All rights reserved.
Motivated by problems in molecular biosciences wherein the evaluation of entropy of a molecular system is important for understanding its thermodynamic properties, we consider the efficient estimation of entropy of a multivariate normal distribution having unknown mean vector and covariance matrix. Based on a random sample, we discuss the problem of estimating the entropy under the quadratic loss function. The best affine equivariant estimator is obtained and, interestingly, it also turns out to be an unbiased estimator and a generalized Bayes estimator. It is established that the best affine equivariant estimator is admissible in the class of estimators that depend on the determinant of the sample covariance matrix alone. The risk improvements of the best affine equivariant estimator over the maximum likelihood estimator (an estimator commonly used in molecular sciences) are obtained numerically and are found to be substantial in higher dimensions, which is commonly the case for atomic coordinates in macromolecules such as proteins. We further establish that even the best affine equivariant estimator is inadmissible and obtain Stein-type and Brewster-Zidek-type estimators dominating it. The Brewster-Zidek-type estimator is shown to be generalized Bayes. (C) 2003 Elsevier Inc. All rights reserved.