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Title: Inference for nonparanormal partial correlation via regularized rank-based nodewise regression Authors:  Yumou Qiu - Iowa State University (United States) [presenting]
Abstract: Partial correlation is a common tool in studying conditional dependence for Gaussian distributed data. However, the partial correlation being zero may not be equivalent to conditional independence under non-Gaussian distributions. We propose a statistical inference procedure for partial correlations under the high-dimensional nonparanormal (NPN) model, where the observed data are normally distributed after certain monotone transformations. The nonparanormal partial correlation is the partial correlation of the normal transformed data under the NPN model, which is a more general measure of conditional dependence. We estimate the NPN partial correlations by regularized nodewise regression based on the empirical ranks of the original data. A multiple testing procedure is proposed to identify the nonzero NPN partial correlations. The proposed method can be carried out by a simple coordinate descent algorithm for lasso optimization. It is easy to implement and computationally more efficient compared to the existing methods for estimating NPN graphical models. Theoretical results are developed to show the asymptotic normality of the proposed estimator and to justify the proposed multiple-testing procedure. Numerical simulations and a case study on brain imaging data demonstrate the utility of the proposed procedure and evaluate its performance compared to the existing methods.