Properties of Multivariate Cauchy and Poly-Cauchy Distributions with Bayesian g-Prior Applications
Properties of Multivariate Cauchy and Poly-Cauchy Distributions with Bayesian g-Prior Applications
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多元柯西分布和聚柯西分布的性质及其贝叶斯 g 先验应用
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
J. Dickey
中科院分区：
文献类型：
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作者：
Gorui Bian;J. Dickey
众所周知，两个独立的柯西随机变量的和按照（缩放的）柯西分布分布。然而，在一般的多元情况下，这种繁殖性质不再成立；本文研究了N ~临界值和充分条件。密度与多个密度的乘积成正比的分布被称为多t分布，或者密度中的两个因素称为双t分布。本文推导了多元双柯西密度的归一化常数和低阶矩的简单数学形式，当两个柯西密度因子满足上述条件时。然后将这些形式应用于具有独立cauchy型g先验分布的线性多元回归抽样模型中，获得多元正态位置参数和斜率系数的新贝叶斯估计。新的估计量是自适应的，并且与通常使用自然共轭先验分布获得的贝叶斯估计有很大的不同。
The sum of two independent Cauchy random variables is well-known to be distributed according to a ( scaled) Cauchy distribution. This reproductive property is no longer tenable, however, in the general multivariate case; n~ssary and sufficient conditions are here investigated. A distribution whose density is proportional to a product oft-densities has been called a poly-t distribution, or double-t for two factors in the density. Simple mathematical forms for the normalizing constant and the lower-order moments of the multivariate double-Cauchy density are here derived when the two Cauchy-density factors satisfy the aforementioned conditions. These forms are then applied to obtain new Bayesian estimates of the multivariate normal location parameter and slope coefficients in the linear multiple regression sampling model with independent Cauchy-type g-prior distributions. The new estimators are adaptive, and differ substantially from the usual Bayesian estimates obtained using natural conjugate prior distributions.