On the fractional moments of a truncated centered multivariate normal distribution
On the fractional moments of a truncated centered multivariate normal distribution
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关于截断中心多元正态分布的分数矩
DOI：
10.1080/03610918.2020.1725821
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Kazuki Nakamoto and Tomonari Sei
中科院分区：
文献类型：
--
作者：
Mitsunori Ogawa;Kazuki Nakamoto and Tomonari Sei
本文研究了截尾中心多元正态分布的分数阶矩，重点讨论了分数阶矩的计算。我们开发的计算方法，包括基于完整梯度法，二阶拉普拉斯近似，和蒙特卡罗方法。这些方法使我们能够计算高阶分数阶矩，而无需计算多重积分。通过数值实验，我们研究了它们的性能。一些应用，包括强大的图形建模的基础上替代多元t分布，也提出了。
In this paper, we study the fractional moments of a truncated centered multivariate normal distribution, with a focus on their computation. We develop computational methods, including ones based on the holonomic gradient method, the second-order Laplace approximation, and the Monte Carlo method. These methods enable us to compute higher order fractional moments without evaluating multiple integrals. Via numerical experiments, we investigate their performances. Some applications, including robust graphical modeling based on the alternative multivariate t-distribution, are also presented.