Reference prior bayes estimator for bivariate normal covariance matrix with risk comparison
Reference prior bayes estimator for bivariate normal covariance matrix with risk comparison
复制标题
带风险比较的双变量正态协方差矩阵的参考先验贝叶斯估计器
DOI：
10.1080/03610929708832042
复制
发表时间：
1997
影响因子：
0.8
通讯作者：
Hiroki Ishibayashi
中科院分区：
文献类型：
--
作者：
N. Sugiura;Hiroki Ishibayashi
本文给出了熵损失下二元正态协方差矩阵的Yang和Berger（1994）的参考先验Bayes估计在自由度为偶数时的Legendre多项式形式和在一般情况下的超几何函数形式的显式表达式。得到了二元Wishart矩阵的特征根比的密度函数的有限级数表达式，并将其精确风险与James-Stein极小极大估计及其它正交同变估计的精确风险进行了比较.数值结果表明，当协方差矩阵的最大与最小总体特征根之比位于区间[1，∞]的中间时，参考先验Bayes估计在所比较的同变估计类中具有最小的风险.当比值较大时，它比James-Stein极大极小估计具有更大的风险。此外，当自由度为20且比率在4和8之间时，它具有比MLE更大的风险。
The explicit form of the reference prior bayes estimator due to Yang and Ber-ger (1994) for bivariate normal covariance matrix under entropy loss is given in terms of Legendre polynomials when degrees of freedom is even and in terms of hypergeometric functions in general case. The finite series expression of the density function of the ratio of latent roots of bivariate Wishart matrix is obtained and the exact risk is compared with those of James-Stein minimax estimator and other orthogonally equivariant estimators. It is found numerically that the reference prior bayes estimator has the smallest risk among the class of equivariant estimators compared, when the ratio of the largest to the smallest population latent roots of covariance matrix lies in the middle of the interval [1, ∞]. It has larger risk than that of James-Stein minimax estimator when the ratio is large. Moreover it has larger risk than that of MLE when, for instance, degrees of freedom is 20 and the ratio lies between 4 and 8.