Local and Global Inference for High Dimensional Nonparanormal Graphical Models
This work addresses uncertainty quantification in graphical models for high-dimensional data analysis, offering a method that extends existing frameworks without relying on Gaussian assumptions, though it is incremental in nature.
The paper tackles the problem of quantifying uncertainty in high-dimensional nonparanormal graphical models by proposing a unified framework for local and global inference, including testing single edges and constructing uniform confidence subgraphs, with results showing theoretical properties verified through numerical experiments and real data analysis.
This paper proposes a unified framework to quantify local and global inferential uncertainty for high dimensional nonparanormal graphical models. In particular, we consider the problems of testing the presence of a single edge and constructing a uniform confidence subgraph. Due to the presence of unknown marginal transformations, we propose a pseudo likelihood based inferential approach. In sharp contrast to the existing high dimensional score test method, our method is free of tuning parameters given an initial estimator, and extends the scope of the existing likelihood based inferential framework. Furthermore, we propose a U-statistic multiplier bootstrap method to construct the confidence subgraph. We show that the constructed subgraph is contained in the true graph with probability greater than a given nominal level. Compared with existing methods for constructing confidence subgraphs, our method does not rely on Gaussian or sub-Gaussian assumptions. The theoretical properties of the proposed inferential methods are verified by thorough numerical experiments and real data analysis.