Abstract:
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In this paper, we propose a unified asymptotic inference framework for Gaussian copula graphical models, to test the presence of a specific edge, and the whole graph. Since the likelihood function of the Gaussian copula graphical model depends on the unknown marginal transformation functions, we propose to analyze its pseudo likelihood function. There are mainly two challenges when analyzing the pseudo likelihood function. The first challenge is that the pseudo likelihood function is a nonlinear function of U-statistics. The second challenge is that the pseudo score function of the parameter of interest is not asymptotically normal. We propose to decorrelate the pseudo score function of the parameter of interest with the score function of the nuisance parameters, and present a score test statistic based on the decorrelated pseudo score function. We establish the limiting distribution of the resulting score test statistic under both null hypothesis and the local alternative hypothesis. The theory provides asymptotic guarantees on the type I error as well as the local power of the score test. Based on the score test statistic, we further derive a Wald test statistic using an one-st
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