基于概率积分变换与似然比的高维相关性检验

Multi-dimensional correlation test based on the probability integral translation and likelihood ratio

高维相关性的拟合优度检验是Copula尤其是高维Copula实践应用中遇到的复杂课题。为了解决这一难题,该文将Berkowitz在2001年提出的基于概率积分变换的似然比检验单变量分布的方法推广用来做多变量分布的拟合优度检验,特别是用来检验高维copula的拟合优度。通过Monte Carlo模拟对比实验,结果表明基于概率积分变换的似然比检验统计量对高维相关性的拟合优度具有很强的检测能力,同时对小样本数据同样有效。

The goodness-of-fit test for multi-dimensional correlations is a complex problem. In order to solve this problem, this paper generalizes the likelihood ratio method based on the probability integral translation for a single stochastic variable distribution, which developed by Berkowitz in 2001, to the ease of multi-variable distributions. Monte Carlo experiments show that the likelihood ratio test based on the probability integral translation is robust for the goodness-of-fit test for multi-dimensional correlations and is especially effective with small samples.