高维精度矩阵的同时推断方法

Simultaneous inference for a high-dimensional precision matrix

高斯图模型广泛地应用于网络数据的分析。虽然目前已经有了很多估计高斯图模型参数的方法,但高斯图模型的同时推断问题也具有重要的意义。我们提出了一种自助方法来进行高斯图模型的同时统计推断。我们的同时推断方法适用于大规模的图模型,并允许感兴趣的参数向量的维数大于样本数量。我们证明了同时检验的结果能够渐近地达到了预设的显著性水平,而进一步的仿真实验验证了所提方法的有效性。

Gaussian graphical models have been widely used for network data analysis.Although various methods exist for estimating the parameters,simultaneous inference is essential for graphical models.In this study,we propose a bootstrap procedure to conduct simultaneous inference for Gaussian graphical models.The simultaneous inference procedure is applied to large-scale graphical models and allows the dimension of the parameter vector of interest to exceed the sample size.We prove that the simultaneous test achieves a pre-set significance level asymptotically.Further simulation studies demonstrate the effectiveness of the proposed methods.