标题： 关于多元 $t$ 分布的条件分布 显示英文标题

标题： On the Conditional Distribution of the Multivariate $t$ Distribution

摘要： 作为正态分布的替代选择，$t$分布在处理含有异常值或厚尾的数据时被广泛应用于稳健性分析。 Kotz 和 Nadarajah 的书中详细记录了多元$t$分布的性质，但该书却得出了关于多元$t$分布条件分布的错误结论。 先前的研究已认识到，多元$t$分布的条件分布同样遵循多元$t$分布。 我们提供了一个直观的证明方法，而无需直接操作多元$t$分布复杂密度函数。 显示英文摘要

摘要： As alternatives to the normal distributions, $t$ distributions are widely applied in robust analysis for data with outliers or heavy tails. The properties of the multivariate $t$ distribution are well documented in Kotz and Nadarajah's book, which, however, states a wrong conclusion about the conditional distribution of the multivariate $t$ distribution. Previous literature has recognized that the conditional distribution of the multivariate $t$ distribution also follows the multivariate $t$ distribution. We provide an intuitive proof without directly manipulating the complicated density function of the multivariate $t$ distribution.